Projectile Motion Competition

Ready, set….calculate!

Woo Hoo! New Equation!

• The Range Equation:• Range = (V0

2 / g) * sin(2θ)• Describes how far downrange a projectile will

land if shot at an angle θ and an initial velocity of V0.

Problem 1: (starting out easy…)

• A punter kicks a football at an angle of 400 from the horizontal at an initial velocity of 60m/s. • What are V0X and V0Y?• V0X = 45.96m/s, V0Y = 38.568m/s

…And then…

• Same football player. Same 400 from the horizontal and same 60m/s. • How long is the ball in the air?• T = 7.87 sec

…And then…

• The aforementioned punter still kicks the ball at 60m/s at 400 from the horizontal. • How high does the ball go?• Height = 75.89m

…And then…

• Same player yet again. 400 from the horizontal, 60m/s. • How far downfield does the

ball go?• Distance = 361.7 m

…And then…

• A boy stands on a cliff that is 300 m high. He throws a baseball 40m/s horizontally.

• How long does it take the ball to hit the ground?

• How far does it land (horizontally) from the base of the cliff?

• Time = 7.82 sec• Distance = 312.8 meters

…And then…

• Two miscreants with a catapult seek to destroy a garniture 100 meters away.

• If the catapult throws its ammunition at an angle of 300 above the horizontal, with what initial velocity must the rock have in order to hit the target?

• V0 = 33.64m/s

…And then…• Patches O'Houlihan maintains that if you can

dodge a wrench, you can dodge a ball. • If he throws a wrench at your forehead from

15 meters away at a speed of 36 m/s, how long do you have to get out of the way?

• If it were thrown horizontally, how far has it fallen vertically before it reaches you?

• Reaction time = 0.416 m/s, • Vertical distance = 0.85 meters

…And then…

• Wile E. Coyote (Road-Runnerus digestus) attempts to catch his prey by donning a pair of rocket skates. He accidentally hits a ramp of angle 250 at a speed of 140 m/s. Assume his skates run out of gas the moment he leaves the ramp.

• Will he clear a cliff face 33.5m higher than the lip of the ramp that is 75 meters away? If so, by how much and if not, by how little?

• No. At 75 m, you are 33.19m high.