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Projectile Motion Competition. Ready, set….calculate!. Woo Hoo ! New Equation!. The Range Equation: Range = (V 0 2 / g) * sin(2 θ ) Describes how far downrange a projectile will land if shot at an angle θ and an initial velocity of V 0 . Problem 1: (starting out easy…).

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Projectile motion competition

Projectile Motion Competition

Ready, set….calculate!


Woo hoo new equation
Woo Hoo! New Equation!

  • 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.


Problem 1 starting out easy
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
…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 then1
…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 then2
…And then…

  • Same player yet again. 400 from the horizontal, 60m/s.

  • How far downfield does the ball go?

  • Distance = 361.7 m


And then3
…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 then4
…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 then5
…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 then6
…And then…

  • 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.


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