Question

When William Tell shot the apple off his son's head, the arrow remained stuck in the apple, which means the collision between the arrow and apple was totally inelastic. Suppose that the velocity of the arrow was horizontal at 75 m/s before it hit, the mass of the arrow was 45 g, and the mass of the apple was 190 g. Suppose Tell's son was 1.4 m high.

A) Calculate the velocity of the apple and arrow directly after the collision.
B) Calculate how far behind the son the apple and arrow landed on the ground.

Answer 1

(A) Use conservation of momentum to calculate the horizontal velocity component Vx of the apple with embedded arrow after the apple is hit.
45*75 = (45 + 190) Vx

Use the height of the boy (H) to calculate how long the apple takes to hit the ground. Call that time T.
(1/2)gT^2 = H

Then multiply V and T for the answer to part (B).

Answer 2

drwls,

i think your way of solving the problem is incorrect. my online homework rejected your answers.

From your equations I concluded:
Vx=33.5 m/s, Vy=0
V=(Vx^2+Vy^2)^(1/2) = 33.5 m/s

X=v*(2h/g)^(1/2) = (2*1.4/9.81)^(1/2)
= 17.9 m

Unfortunately, these answers are wrong.

Answer 3

Your Vx is wrong, and is not given by the formula I wrote. Your T is correct.