PROJECTILE MOTION CHARACTERISTICSThe projectile has:•a constant horizontal velocity and•a vertical velocity that changes uniformly under the influence of gravity.
If an object is projected horizontally, its motion can bestbe described by considering its horizontal and verticalmotion separately. In the figure we can see that thevertical velocity and position increase with time as thoseof a free-falling body.Note that thehorizontal distanceincreases linearlywith time, indicatinga constanthorizontal velocity.
Take this basketball shot as an example. Notice thehorizontal velocity of the ball. Look at the spacing of thevertical lines which mark the position of the ball every 10th ofa second. The spacing is quite consistent, which indicates aconstant horizontal velocity.
HORIZONTAL MOTIONVelocity (vx) is constant Velocity x vx t Distance x vx t Time x t vx
VERTICAL MOTIONVelocity (vy) increases under the acceleration due to gravity. Velocity voy 0 vy gt Distance 1 2 y gt 2 Time 2y t g
RESULTANT VELOCITYThe resultant velocity can be found using the Pythagoreantheorem. 2 2 vR (vx ) (v y )
3.6 A ball is thrown horizontally with a velocity of 12 m/s.How far has the ball fallen 2 s later? HORIZONTAL VERTICAL vox = 12 m/s voy = 0 m/s t=2s g = 9.8 m/s2 t=2s vox = vx y = ½ gt2 x = vx t = ½ (9.8)(2)2 = 12(2) = 19.6 m = 24 m
3.7 A rifle with a muzzle velocity of 200 m/s is fired with its barrelhorizontally at a height of 1.5 m above the ground.a. How long is the bullet in the air? HORIZONTAL VERTICAL vox = 200 m/s voy = 0 m/s y = 1.5 m 1 2 y gt g = 9.8 m/s2 2 2y 2(1.5) t = 0.55 s g 9 .8
b. How far away from the rifle does the bullet strike the ground? x = vx t = 200(0.55) = 110 m
3.8 A ball is rolled off the edge of a table 1 m high with a horizontalvelocity of 1.8 m/s. With what velocity does it strike the floor? HORIZONTAL VERTICAL vox = 1.8 m/s voy = 0 m/s y=1m g = 9.8 m/s2 2 2 We need to find the resultant velocity: v f vx vy Where: 1 2 vx = vox = 1.8 m/s y gt 2 vy = voy + gt 2y 2(1) t = 0.45 s g 9 .8
THE MONKEY AND THE ZOOKEEPERThe monkey spends most of its day hangingfrom a branch of a tree.The zookeeper feeds the monkey byshooting bananas from a banana cannon tothe monkey in the tree.The monkey usually drops from the tree themoment that the banana leaves the muzzleof the cannon.The zookeeper is faced with the dilemma ofwhere to aim the banana cannon in order tofeed the monkey. If the monkey lets go ofthe tree the moment that the banana isfired, then where should he aim the bananacannon?
The zookeeper aims above the monkey (perhaps hepresumes that gravity will accelerate the banana downwardsuch that it hits the monkey). What would be the path of thebanana? Would the banana hit the monkey? Since both banana and monkey experience the same acceleration each will fall equal amounts and the banana misses the monkey, moving over his head.
The zookeeper aimsat the monkey andshoots the banana.Since both bananaand monkeyexperience the sameacceleration each willfall equal amounts the The key to the zookeepersbanana reaches the dilemma is to aim directly atmonkey! the monkey. SHOOT THE MONKEY