An arrow is fired with a speed of 24.0 m/s at a block of Styrofoam resting on a

Question

An arrow is fired with a speed of 24.0 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 1400 m/s2 and the block's acceleration has a magnitude of 450 m/s2

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

what is the common speed of the arrow and the block?

how far does the block penetrate into the arrow?

I don't need the answers. what i need is for someone to explain what is going on in this problem.

I don't understand why i need to find the common speed in the first part to find when the arrow stops moving and i dont understand anything about how to find how far the arrow penetrates.

Explanation / Answer

t = (24 - Vb) /1400 time for arrow to slow to final speed of block Vb = 450 t final speed of block (and arrow - common speed) 1400 t = 24 - 450 t combining equations t = .0253 sec time specified above Sa = Va t - 1/2 * 1400 t^2 distance arrow moves in time t Sb - 1/2 * 450 * t^2 distance block moves in time t Sa - Sb = penetration of arrow

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