An arrow is fired with a speed of 22.0 m/s at a block of Styrofoam resting on a

Question

An arrow is fired with a speed of 22.0 m/s at a block of Styrofoam resting on a smooth surface. The arrow penetrates a certain distance into the block before coming to rest relative to it. During this process the arrow's deceleration has a magnitude of 1600 m/s2 and the block's acceleration has a magnitude of 450 m/s2.

A)How long does it take for the arrow to stop moving with respect to the block?

B)What is the common speed of the arrow and block when this happens?

C)How far into the block does the arrow penetrate?

Explanation / Answer

Assuming the 2 accelerations given are relative to the observer (the one firing the arrow) the acceleration of the arrow relative to the block would be:

a = -1600 + 450 m/s² = -1150 m/s²  

A) By using the quation of motion: v=vo+at

0=22-1150*t

t=0.019 sec

B) The commmon speed for the arrow and the block is 22m/s.

C) By using the equation of motion: v² - (vo)² = 2ax

0 - (22.0 m/s)² = 2*(-1150 m/s²)*x

x = 0.21 m

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