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Projectile Motion Competition

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Projectile Motion Competition

Ready, set….calculate!

- The Range Equation:
- Range = (V02 / g) * sin(2θ)
- Describes how far downrange a projectile will land if shot at an angle θ and an initial velocity of V0.

- 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

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

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

- Same player yet again. 400 from the horizontal, 60m/s.
- How far downfield does the ball go?
- Distance = 361.7 m

- 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

- 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

- 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

- Wile E. Coyote (Road-Runnerusdigestus) 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.