2. Projectile Motion
Projectile motion, or the free fall, is motion in two dimensions. A
projectile is thrown into the air (vertical direction) with an initial
velocity and then moves (horizontal direction) under the force of the
gravity.
The path that the projectile travels is called a trajectory.
3. Components of projectile motion
Projectile motion is made up of two components; (1) horizontal motion and (2)
the vertical motion.
The horizontal motion of projectile motion is moving at uniform motion . This
means that it is not accelerating or that it moves with the same change in
distance over time. The formula for it is shown, where v is the horizontal speed,
d, is the change in the horizontal distance, and t is the time it took to travel or
cover that distance:
v=
𝑑
𝑡
When the body does not move with uniform motion, it changes it velocity.
Velocity, as a vector, changes two ways (a) by changing its direction or (b) by
changing its magnitude, which is its speed. The speed changes either by speeding
up or by slowing down.
4. When body is moving with uniform change in its velocity, it is moving with
uniform acceleration. Acceleration is also a vector that is defined by its
direction and its magnitude. Recall that the equation describe the motion
of uniformly accelerated body are.
5. The formula as to describe its motion would be the formula for uniform
acceleration except that the acceleration is –g. The formula would be
6. Look at the figure 11.3. the acceleration due to gravity is negative because
even as you throw a body upward. (A) it slow down at a constant rate,
consistent with the acceleration due to gravity. The body would slow down
so much that bit would literally stop and change direction because of the
acceleration due to gravity. (B) then as it goes down, it speeds up but the
acceleration due to gravity is still negative because the body is now falling
downward ( C).
7. SAMPLE PROBLEM:
Raindrops fall from a height of 2000 meters above the ground. How fast are they
moving right before the hit the ground?
GRESA METHOD:
Given: d= -2000 answer: Vfy= 197.99 m/s
g= 9.8 m/s ^2
Vi= 0
Required: Vf=?
Equation : Vfy ^2 = Viy ^2 – 2gd
Solution :
8. Theoretically, the velocity of the raindrop coming from height of 2000 m is
197.99 m/s , which is more than twice the speed of the fastest wind speed
of super typhoon Yolanda (87.5 m/s) . The presence of air resistance is
strong enough to counter the pull of gravity, so that the raindrop stops
accelerating downward and begins to move at constant velocity. The
velocity the body attain is called terminal velocity, which is the speed
attained when the drag is equal to weight and the body stops accelerating
due to gravity.
9. Sample problem
How fast is a ball moving when falling from rest and hits the ground 1.5
seconds later?
Givens
vi = 0 m/s
a = 10 m/s2 down
t = 1.5 s
Required: vf = ?
Equation:
vf = vi + at
Solution :
vf = 0 + (10)(1.5)
Answer: vf = 15 m/s down
10. ACTIVITY:
1. How long does it take a ball to hit the ground when dropped from
40 meters?
2. What is the final velocity of a ball the moment before it strikes the
ground from 40 meters?
11. Activity 1: Horizontal Motion
1. A bowling ball is rolled off the top of a cliff with an initial horizontal velocity of 6.0 m/s . If
the cliff is 100. m above the ground, determine the ball’s time of flight.
A. The ball’s time of flight .
B. the ball’s range
2. A helicopter flying horizontally at a velocity of 25 m/s drops a mailbag from a height of
15m to a letter carrier waiting on the ground below.
A. How long will the bag take to fall to the ground?
B. How far in advance of the letter carrier must the bag be released so that it lands at
her feet?
12. Exercise:
Ms. Swanson throws a tomato horizontally out of an open
window with a velocity of 3.0 m/s. If the window is 10. m above
the ground, how far away from the building must Ms. Reichling
stand to catch the ball at ground level?
