PHYSICS 1A MIDTERM REMEDIATION           TUTORIAL
WHY REMEDIATE?•   You must pass the midterm exam in order to work on the module based lessons after the    Holiday Break.•...
FORMAT•   Each sections will give you the following:     1. A list of things your are expected to be able to do     2. A l...
SECTION 1- BASIC TOOLSYou should be able to:Define hypothesis as a prediction which can be tested.Write a hypothesis as an...
BASIC TOOLS ACTIVITIES-PAGE 1• Read pages 2-4 in your book- this describes the  scientific methods and hypotheses.• On pag...
BASIC TOOLS ACTIVITIES-PAGE 2• One page 4, the correct answer to the question is letter  A. This is the only option which ...
BASIC TOOLS ACTIVITIES- PAGE 3• Go to  http://www.youtube.com/watch?v=n6Vmk5dMdM8, and  watch the video on writing a hypot...
BASIC TOOLS ACTIVITIES- PAGE 4•   Case Study 1-•   Larry is trying to determine if using a larger concentration of fertili...
BASIC TOOLS ACTIVITIES- PAGE 5 (ANSWERS)•   Case Study 1-•   Larry is trying to determine if using a larger concentration ...
BASIC TOOLS ACTIVITIES- PAGE 6• Go to http://www.youtube.com/watch?v=tK2mBsSb3uw  and watch the video on parts of an exper...
BASIC TOOLS- PRACTICE QUESTIONS•   To test a scientific hypothesis you would•   a.     use the results of only the experim...
ANSWER• The answer to the previous question was ―d‖. Can you  explain why?
BASIC TOOLS- PRACTICE QUESTION 2An athlete is trying to improve their time in the mile run by increasing their intake of w...
ANSWERSAn athlete is trying to improve their time in the mile run by increasing their intake of water.They make the hypoth...
BASIC TOOLS-PRACTICE QUESTIONSConvert the following units:144 inches to feet45 pounds to kg150 minutes to hours
ANSWERSConvert the following units:144 inches to feet 12 feet45 pounds to kg 20.5 kg150 minutes to hours 2.5 hour
SECTION 2- KINEMATICSYou should be able to:Differentiate between speed and velocity.Define speed as a distance over time.C...
KINEMATICS ACTIVITIES- PAGE 1• Read pages 47-58 in your book. Focus on the vocabulary  words given above, and try to answe...
KINEMATICS- PRACTICE PROBLEMSOne possible unit of speed isa.         miles per hour.b.         light years per century.c. ...
ANSWER• The answer is ―d‖. Speed must be some unit of distance over some unit of  time, and all of the options are in this...
KINEMATICS- PRACTICE PROBLEMSAcceleration is defined as the CHANGE ina.        time it takes to move from one place to ano...
ANSWER• The answer is ―d‖, acceleration is change in velocity  divided by the time interval. What can happen for an  objec...
KINEMATICS- PRACTICE PROBLEMSSuppose you are in a car that is going around a curve. The speedometer reads a constant 30mil...
ANSWER• The answer is ―c‖. Can you explain why? If not, see  Mr. White.
KINEMATICS- PRACTICE PROBLEMSIn the absence of air resistance, objects fall at constanta.         speed.b.         velocit...
ANSWER• The correct answer is ―C‖.
KINEMATICS- PRACTICE PROBLEMSIf you drop a feather and a coin at the same time in a tube filled with air, which will reach...
SECTION 3- FORCESYou should be able to:Define net force and calculate the net force acting on an object using given forces...
FORCES ACTIVITIES• 1. Read pages 13-17 in your book. Try to answer all blue box  questions.  2. Go to  http://www.physicsc...
FORCES PRACTICE PROBLEMSA 7-N force and a 12-N force act on an object in opposite directions. What is the net force onthe ...
ANSWER• The answer should be 5N. Why?
PRACTICE PROBLEMSEquilibrium occurs whena.        all the forces acting on an object are balanced.b.        the sum of the...
ANSWER•E
PRACTICE PROBLEMS• Draw a free body diagram indicating a force of 25 N to the right, 35 N up, and  unknown forces to the l...
ANSWER•   Left 35 N•   Down  35 N
PRACTICE PROBLEMS•   Draw a free body diagram indicating a force of 750 N to the right, 350 N up, and    unknown forces to...
ANSWER•   Left 750 N•   Down  600 N
SECTION 3- NEWTON’S LAWSYou should be able to:Define inertia as resistance to change in motion.Use the Law of Inertia to d...
NEWTON ACTIVITIES- PAGE 11. Read pages 33-39 in your book. Try to answer all blue box questions.2. Go to http://www.physic...
NEWTON ACTIVITIES- PAGE 2• 5. Read pages 87-89 in your book and try all blue box questions.  6. Go to http://www.physicscl...
PRACTICE PROBLEMSAfter a cannonball is fired into frictionless space, the amount of force needed to keep it goingequalsa. ...
PRACTICE PROBLEMSAfter a cannonball is fired into frictionless space, the amount of force needed to keep it goingequalsa. ...
PRACTICE PROBLEMSThe law of inertia applies toa.         objects at rest.b.         moving objects.c.         both moving ...
PRACTICE PROBLEMSThe law of inertia applies toa.         objects at rest.b.         moving objects.c.         both moving ...
PRACTICE PROBLEMSAn object following a straight-line path at constant speeda.         has no forces acting on it.b.       ...
PRACTICE PROBLEMSAn object following a straight-line path at constant speeda.         has no forces acting on it.b.       ...
PRACTICE PROBLEMSYou would have the largest mass of gold if your chunk of gold weighed 1 N ona.        Earth.b.        Jup...
PRACTICE PROBLEMSYou would have the largest mass of gold if your chunk of gold weighed 1 N ona.        Earth.b.        Jup...
PRACTICE PROBLEMSThe acceleration produced by a net force on an object isa.         inversely proportional to the mass of ...
PRACTICE PROBLEMSThe acceleration produced by a net force on an object isa.         inversely proportional to the mass of ...
PRACTICE PROBLEMSIf the force acting on a cart doubles, what happens to the carts acceleration?a.         It quarters.b.  ...
PRACTICE PROBLEMSIf the force acting on a cart doubles, what happens to the carts acceleration?a.         It quarters.b.  ...
PRACTICE PROBLEMSAn archer shoots an arrow. Consider the action force to be the bowstring against the arrow.The reaction t...
PRACTICE PROBLEMSAn archer shoots an arrow. Consider the action force to be the bowstring against the arrow.The reaction t...
PROJECTILES-SECTION 5You should be able to:Explain the difference between a vector and scalar quantity.Add vectors in one ...
PROJECTILES- ACTIVITIES1. Read pages 69-79 in your book and complete all bluebox questions and check answers.2. Complete t...
PRACTICE PROBLEMSThe horizontal component of a projectiles velocity is independent ofa.         the range of the projectil...
PRACTICE PROBLEMSThe horizontal component of a projectiles velocity is independent ofa.         the range of the projectil...
PRACTICE PROBLEMSIn the absence of air resistance, the angle at which a thrown ball will go the farthest isa.         15 d...
PRACTICE PROBLEMSIn the absence of air resistance, the angle at which a thrown ball will go the farthest isa.         15 d...
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Physics 1 a midterm remediation tutorial2

  1. 1. PHYSICS 1A MIDTERM REMEDIATION TUTORIAL
  2. 2. WHY REMEDIATE?• You must pass the midterm exam in order to work on the module based lessons after the Holiday Break.• This tutorial should prepare you to retake the midterm in order to pass it• YOU are responsible to understanding the material, so take your time going through the tutorial• If you understand a concept, don’t spend a lot of time watching videos that you already understand!
  3. 3. FORMAT• Each sections will give you the following: 1. A list of things your are expected to be able to do 2. A list of vocabulary words you need to make flashcards for and commit to memory 3. A list of activities for you to re-learn the content 4. A list of practice ―test type‖ questions that you should be able to answer correctly before moving on.
  4. 4. SECTION 1- BASIC TOOLSYou should be able to:Define hypothesis as a prediction which can be tested.Write a hypothesis as an if/then statement which can be tested.Identify the parts of an experiment or design an experiment to test a specific hypothesis.Convert from one basic unit to another using dimensional analysis.Make flashcards with the following definitions and memorize them: Hypothesis- a testable prediction Independent Variable- the variable that is being tested Dependent Variable- the variable that changes due to the independent variable Control- the trial used for comparison Constant- things that don’t change in an experiment
  5. 5. BASIC TOOLS ACTIVITIES-PAGE 1• Read pages 2-4 in your book- this describes the scientific methods and hypotheses.• On page 4 there is a blue box with a question. Answer that question, and check to make sure you chose the correct answer.
  6. 6. BASIC TOOLS ACTIVITIES-PAGE 2• One page 4, the correct answer to the question is letter A. This is the only option which is TESTABLE.
  7. 7. BASIC TOOLS ACTIVITIES- PAGE 3• Go to http://www.youtube.com/watch?v=n6Vmk5dMdM8, and watch the video on writing a hypothesis.
  8. 8. BASIC TOOLS ACTIVITIES- PAGE 4• Case Study 1-• Larry is trying to determine if using a larger concentration of fertilizer on his grass will make the grass grow faster. He lines off five sections of his yard and uses different concentration of fertilizer on each section. He uses a concentration of 44 gpL (grams per liter) on section 1, a concentration of 87 gpL on section 2, a concentration of 121 gpL on section 3 and a concentration of 189 gpL on section 4. He leaves section 5 alone with no fertilizer. He finds that section 1 grows at a rate of .27 inches/day, section 2 grows at .35 inches/day, section 3 grows .29 inches/day and section 4 completely dies. • What do you think Larry’s hypothesis was? • What should Larry’s conclusion be? • What was Larry’s independent variable? • What was Larry’s dependent variable? • What was Larry’s control? • List at least 8 things that Larry should have kept constant?
  9. 9. BASIC TOOLS ACTIVITIES- PAGE 5 (ANSWERS)• Case Study 1-• Larry is trying to determine if using a larger concentration of fertilizer on his grass will make the grass grow faster. He lines off five sections of his yard and uses different concentration of fertilizer on each section. He uses a concentration of 44 gpL (grams per liter) on section 1, a concentration of 87 gpL on section 2, a concentration of 121 gpL on section 3 and a concentration of 189 gpL on section 4. He leaves section 5 alone with no fertilizer. He finds that section 1 grows at a rate of .27 inches/day, section 2 grows at .35 inches/day, section 3 grows .29 inches/day and section 4 completely dies. • What do you think Larry’s hypothesis was? If I use a larger concentration of fertilizer my grass will grow faster • What should Larry’s conclusion be? Increased concentration does not make the grass grow faster • What was Larry’s independent variable? Concentration of fertilizer • What was Larry’s dependent variable? Rate of grass growth • What was Larry’s control? Section 5- no fertlilizer • List at least 8 things that Larry should have kept constant? Type of grass, location, temperature, type of fertilizer, soil type, measuring device, amount of water, measurement time
  10. 10. BASIC TOOLS ACTIVITIES- PAGE 6• Go to http://www.youtube.com/watch?v=tK2mBsSb3uw and watch the video on parts of an experiment.• Go to http://www.youtube.com/watch?v=XKCZn5MLKvk and review unit conversions.
  11. 11. BASIC TOOLS- PRACTICE QUESTIONS• To test a scientific hypothesis you would• a. use the results of only the experiments that confirm the hypothesis.• b. set up an experiment and look at the results.• c. find the best result and report only that result.• d. set up many experiments and look at the results.• e. perform any physics experiment and look at the results.
  12. 12. ANSWER• The answer to the previous question was ―d‖. Can you explain why?
  13. 13. BASIC TOOLS- PRACTICE QUESTION 2An athlete is trying to improve their time in the mile run by increasing their intake of water.They make the hypothesis that as they increase the amount of water they drink within 1 hourof race time, they will run better. On six days in a row, they run a timed mile run. Day 1, theydrink no water before the race. They drink 4 ounces on day 2, 8 ounces on day 3, 12 ounceson day 4, 16 ounces on day 5 and 20 ounces on day 6.a.) Identify the independent variable-b.) Idenitify the dependent variable-c.) Idenitfy the control-d.) Name three things that should be kept constant that are not identified in the description ofthe experiment.
  14. 14. ANSWERSAn athlete is trying to improve their time in the mile run by increasing their intake of water.They make the hypothesis that as they increase the amount of water they drink within 1 hourof race time, they will run better. On six days in a row, they run a timed mile run. Day 1, theydrink no water before the race. They drink 4 ounces on day 2, 8 ounces on day 3, 12 ounceson day 4, 16 ounces on day 5 and 20 ounces on day 6.a.) Identify the independent variable- Amount of water intakeb.) Idenitify the dependent variable- mile timec.) Idenitfy the control- trial with no waterd.) Name three things that should be kept constant that are not identified in the description ofthe experiment. Shoes, running track, time of day
  15. 15. BASIC TOOLS-PRACTICE QUESTIONSConvert the following units:144 inches to feet45 pounds to kg150 minutes to hours
  16. 16. ANSWERSConvert the following units:144 inches to feet 12 feet45 pounds to kg 20.5 kg150 minutes to hours 2.5 hour
  17. 17. SECTION 2- KINEMATICSYou should be able to:Differentiate between speed and velocity.Define speed as a distance over time.Calculate speed using the equation v=x/t.Identify the correct units for speed, velocity, position and accelerationDefine acceleration and identify the conditions in which an object is accelerating.Explain that an object in free fall is accelerating at a rate of 9.8 m/s 2 regardless of mass.Calculate acceleration using the equation a=v2-v`1/tMake flashcards with the following definitions and memorize them: Speed- rate of distance traveled (distance over time) Velocity- change in position over time (speed with direction) Acceleration- change in velocity over time Free Fall- falling with the only acting force being gravity
  18. 18. KINEMATICS ACTIVITIES- PAGE 1• Read pages 47-58 in your book. Focus on the vocabulary words given above, and try to answer any questions they ask in the book (blue boxes on pages 47, 49, 51, 52 and 53).• Go to http://www.physicsclassroom.com/Class/1DKin/U1L1a.cfm, and follow the tutorial on 1 dimensional kinematics. This will explain the concepts required in this unit. Be sure to try the practice problems for each section.• Go to https://www.khanacademy.org/science/physics/mechanics/v/calc ulating-average-velocity-or-speed and view the video on calculating speed.
  19. 19. KINEMATICS- PRACTICE PROBLEMSOne possible unit of speed isa. miles per hour.b. light years per century.c. kilometers per hour.d. all of the above.e. none of the above.
  20. 20. ANSWER• The answer is ―d‖. Speed must be some unit of distance over some unit of time, and all of the options are in this format.
  21. 21. KINEMATICS- PRACTICE PROBLEMSAcceleration is defined as the CHANGE ina. time it takes to move from one place to another place.b. velocity of an object.c. distance divided by the time interval.d. velocity divided by the time interval.e. time it takes to move from one speed to another speed.
  22. 22. ANSWER• The answer is ―d‖, acceleration is change in velocity divided by the time interval. What can happen for an object to accelerate?
  23. 23. KINEMATICS- PRACTICE PROBLEMSSuppose you are in a car that is going around a curve. The speedometer reads a constant 30miles per hour. Which of the following is NOT true?a. You and the car are accelerating.b. Your acceleration is constantly changing.c. Your velocity is constant.d. Your direction is constantly changing.e. Your speed is constant.
  24. 24. ANSWER• The answer is ―c‖. Can you explain why? If not, see Mr. White.
  25. 25. KINEMATICS- PRACTICE PROBLEMSIn the absence of air resistance, objects fall at constanta. speed.b. velocity.c. acceleration.d. distances each successive second.e. all of the above
  26. 26. ANSWER• The correct answer is ―C‖.
  27. 27. KINEMATICS- PRACTICE PROBLEMSIf you drop a feather and a coin at the same time in a tube filled with air, which will reach thebottom of the tube first?a. The featherb. Neither—they will both reach the bottom at the same time.c. The coin
  28. 28. SECTION 3- FORCESYou should be able to:Define net force and calculate the net force acting on an object using given forces.Draw a free body diagram for an object or fill in missing forces based on a given net force.Explain the difference between balanced and unbalanced forces.Identify equilibrium as another way of saying balanced force.Make flashcards with the following definitions and memorize them:Force- push or a pull one object exerts on anotherNet Force- The sum of all forces acting on an objectBalanced Forces- the sum of all forces is zero, there is no accelerationUnbalanced Forces- the sum of all forces is not zero, there IS an acceleration
  29. 29. FORCES ACTIVITIES• 1. Read pages 13-17 in your book. Try to answer all blue box questions. 2. Go to http://www.physicsclassroom.com/Class/newtlaws/u2l2a.cfm, and work through the four tutorial sections. Be sure to try all practice problems and check your answers. 3. Go to https://www.khanacademy.org/science/physics/mechanics/v/bala nced-and-unbalanced-forces and view the video on balanced and unbalanced forces. 4. Go to http://www.youtube.com/watch?v=93ZLqsDFBo4 and view the video on drawing a free body diagram.
  30. 30. FORCES PRACTICE PROBLEMSA 7-N force and a 12-N force act on an object in opposite directions. What is the net force onthe object?a. 5Nb. 7Nc. 12 Nd. 19 Ne. none of the above
  31. 31. ANSWER• The answer should be 5N. Why?
  32. 32. PRACTICE PROBLEMSEquilibrium occurs whena. all the forces acting on an object are balanced.b. the sum of the +x forces on an object equals the sum of the –x forces.c. the net force on the object is zero.d. the sum of the upward forces equals the sum of the downward forces.e. all of the above
  33. 33. ANSWER•E
  34. 34. PRACTICE PROBLEMS• Draw a free body diagram indicating a force of 25 N to the right, 35 N up, and unknown forces to the left and down.• If the net force on the object is 10N leftward, what should the unknown forces be?
  35. 35. ANSWER• Left 35 N• Down  35 N
  36. 36. PRACTICE PROBLEMS• Draw a free body diagram indicating a force of 750 N to the right, 350 N up, and unknown forces to the left and down.• If the net force on the object is 250 N downward, what should the unknown forces be?
  37. 37. ANSWER• Left 750 N• Down  600 N
  38. 38. SECTION 3- NEWTON’S LAWSYou should be able to:Define inertia as resistance to change in motion.Use the Law of Inertia to describe what happens to an object when the net force is zero.Explain the difference between mass and weight.Use Newton’s Second Law to explain how net force affects acceleration.Use Newton’s Second Law to explain how mass affects acceleration.Use the equation Fnet = ma to calculate net force or acceleration.Use Newton’s Third Law to identify action-reaction pairs.Use Newton’s Third Law to explain that action-reaction pairs are equal in size and opposite indirection.Make flashcards with the following definitions and memorize them:Inertia- resistance to change in motion
  39. 39. NEWTON ACTIVITIES- PAGE 11. Read pages 33-39 in your book. Try to answer all blue box questions.2. Go to http://www.physicsclassroom.com/Class/newtlaws/u2l1a.cfm and gothrough the 4 tutorial sections on Newton’s First Law. Be sure to try all practiceproblems and check answers.3. Go to https://www.khanacademy.org/science/physics/mechanics/v/newton-s-1st-law-of-motion and view the video on Newton’s First law. Go tohttps://www.khanacademy.org/science/physics/mechanics/v/newton-s-first-law-of-motion and view this video as well.4. Go to http://www.youtube.com/watch?v=BwkUNrSCNMg (part 1) andhttp://www.youtube.com/watch?v=Hyw9uNF4nmE (part 2) and view thedemonstrations of inertia.
  40. 40. NEWTON ACTIVITIES- PAGE 2• 5. Read pages 87-89 in your book and try all blue box questions. 6. Go to http://www.physicsclassroom.com/Class/newtlaws/u2l3a.cfm and complete the first 3 sections of the tutorial ONLY. Try all practice problems and check answers. 7. Go to https://www.khanacademy.org/science/physics/mechanics/v/newton- s-second-law-of-motion and view the video on the Second Law. 8. Read pages 107-111 in your book and complete all blue box questions. 9. Go to http://www.physicsclassroom.com/Class/newtlaws/u2l4a.cfm and complete the two tutorials for the Third Law.
  41. 41. PRACTICE PROBLEMSAfter a cannonball is fired into frictionless space, the amount of force needed to keep it goingequalsa. zero, since no force is necessary to keep it moving.b. twice the force with which it was fired.c. one half the force with which it was fired.d. the same amount of force with which it was fired.e. one quarter the force with which it was fired.
  42. 42. PRACTICE PROBLEMSAfter a cannonball is fired into frictionless space, the amount of force needed to keep it goingequalsa. zero, since no force is necessary to keep it moving.b. twice the force with which it was fired.c. one half the force with which it was fired.d. the same amount of force with which it was fired.e. one quarter the force with which it was fired.
  43. 43. PRACTICE PROBLEMSThe law of inertia applies toa. objects at rest.b. moving objects.c. both moving and nonmoving objects.
  44. 44. PRACTICE PROBLEMSThe law of inertia applies toa. objects at rest.b. moving objects.c. both moving and nonmoving objects.
  45. 45. PRACTICE PROBLEMSAn object following a straight-line path at constant speeda. has no forces acting on it.b. has a net force acting on it in the direction of motion.c. has zero acceleration.d. must be moving in a vacuum.e. none of the above
  46. 46. PRACTICE PROBLEMSAn object following a straight-line path at constant speeda. has no forces acting on it.b. has a net force acting on it in the direction of motion.c. has zero acceleration.d. must be moving in a vacuum.e. none of the above
  47. 47. PRACTICE PROBLEMSYou would have the largest mass of gold if your chunk of gold weighed 1 N ona. Earth.b. Jupiter.c. the moon.
  48. 48. PRACTICE PROBLEMSYou would have the largest mass of gold if your chunk of gold weighed 1 N ona. Earth.b. Jupiter.c. the moon.
  49. 49. PRACTICE PROBLEMSThe acceleration produced by a net force on an object isa. inversely proportional to the mass of the object.b. directly proportional to the magnitude of the net force.c. in the same direction as the net force.d. all of the abovee. none of the above
  50. 50. PRACTICE PROBLEMSThe acceleration produced by a net force on an object isa. inversely proportional to the mass of the object.b. directly proportional to the magnitude of the net force.c. in the same direction as the net force.d. all of the abovee. none of the above
  51. 51. PRACTICE PROBLEMSIf the force acting on a cart doubles, what happens to the carts acceleration?a. It quarters.b. It halves.c. It stays the same.d. It doubles.e. It quadruples.
  52. 52. PRACTICE PROBLEMSIf the force acting on a cart doubles, what happens to the carts acceleration?a. It quarters.b. It halves.c. It stays the same.d. It doubles.e. It quadruples.
  53. 53. PRACTICE PROBLEMSAn archer shoots an arrow. Consider the action force to be the bowstring against the arrow.The reaction to this force is thea. arrows push against the bowstring.b. weight of the arrow.c. friction of the ground against the archers feet.d. air resistance against the bow.e. grip of the archers hand on the bow.
  54. 54. PRACTICE PROBLEMSAn archer shoots an arrow. Consider the action force to be the bowstring against the arrow.The reaction to this force is thea. arrows push against the bowstring.b. weight of the arrow.c. friction of the ground against the archers feet.d. air resistance against the bow.e. grip of the archers hand on the bow.
  55. 55. PROJECTILES-SECTION 5You should be able to:Explain the difference between a vector and scalar quantity.Add vectors in one dimension and perpendicular vectors using Pythagorean theorem.Define projectile and identify the range, launch angle, hang time and initial speed.Explain that horizontal component of velocity in a projectile does not accelerate.Explain that the vertical component of velocity in a projectile accelerates downward at 9.8m/s2.Identify the angle of maximum range for a projectile.Make flashcards with the following definitions and memorize them:Projectile- anything thrown or shot in the airRange- Distance traveled in a horizontal directionLaunch angle- the angle at which the projectile is launched
  56. 56. PROJECTILES- ACTIVITIES1. Read pages 69-79 in your book and complete all bluebox questions and check answers.2. Complete the FIRST FIVE tutorials athttp://www.physicsclassroom.com/Class/vectors/u3l2a.cfm. Try all practice problems.
  57. 57. PRACTICE PROBLEMSThe horizontal component of a projectiles velocity is independent ofa. the range of the projectile.b. time.c. the vertical component of its velocity.
  58. 58. PRACTICE PROBLEMSThe horizontal component of a projectiles velocity is independent ofa. the range of the projectile.b. time.c. the vertical component of its velocity.
  59. 59. PRACTICE PROBLEMSIn the absence of air resistance, the angle at which a thrown ball will go the farthest isa. 15 degrees.b. 30 degrees.c. 45 degrees.d. 60 degrees.e. 75 degrees.
  60. 60. PRACTICE PROBLEMSIn the absence of air resistance, the angle at which a thrown ball will go the farthest isa. 15 degrees.b. 30 degrees.c. 45 degrees.d. 60 degrees.e. 75 degrees.

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