Physics Application of Projectile Motion

Question

Wile E. Coyote fires a cannon with an initial speed of 125 m/s at an angle of 37o above the horizontal from the top of a cliff 160 m high.

a. please determine the time to reach maximum height?

b. please determine the maximum height above the base of the cliff reached by the cannon ball.

c. please determine the total time which the cannon ball is in the air before it strikes the base of the cliff.

d. if the road runner is standing 2150m away from the base of the cliff, will Wile E. Coyote finally get the Road Runner with the cannon? Please explain and show your work.

e. what is the final velocity (magnitude and direction) of the cannon ball just before it hits the ground?

f. if the Wile E. Coyote misses the Road Runner, what should the angle of the cannon be in order to hit the Road Runner if all other factors, except for the angle, remained the same?

Answer 1

Since this is a projectile motion question, we want to use kinematic equations to solve.

a) height is in variable y and we know acceleration is 9.8 in the negative y direction. We need to get the y component of velocity which is Vsin(theta). We also know that the ball is at maximum height when Vy=0 because it has to hit zero at the top of the peak before it starts moving downward in the negative direction. Therefore you should use v=viy + at where v=0 viy= visintheta and a = -9.8

b) Now that we know time to get to the peak, use h = viyt + .5at^2 where a= -9.8 , viy=visintheta. It asks for the height from the base so we need to add 160 m to the calculated answer for h.

c) Use the peak of the projectile to calculate the rest of the time it takes to hit the ground. Use delta y as your calculated totat height answer from part b, vi=0 and we are solving for t in the equation delta y = vit + .5at^2. Add this time to the time you found in part a to get total time.

d) We need to calculate delta x now that we know total flying time. There is no acceleration in the x direction so a =0, vix= vicostheta. Therefor Delta x = vix (t from part c). If this doesn't equal 2150 than he will not have been hit.

e) vxfinal = vix because there is no acceleration. vyfinal = viy +at where t is total trajectory time. The angle is given by arctan (vyfinal/vxfinal).

f) The condition must be that delta x = 2150 and that time and velocity are constant. We can solve using 2150=vicos(new angle) t. Divide by vi (t) and take the cos^-1 to find theta.