Calculating Deceleration and Penetration Distance of Arrow in Styrofoam Block

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An arrow traveling at 22.0 m/s penetrates a Styrofoam block, decelerating at 1570 m/s² while the block accelerates at 450 m/s². To determine how long it takes for the arrow to stop relative to the block, the appropriate equations of motion must be applied. The common speed of both the arrow and block at the point of stopping can be calculated using their respective accelerations. Additionally, the penetration distance into the block can be found by integrating the motion equations. A clear understanding of kinematic equations is essential to solve these problems effectively.
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Homework Statement


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 1570 m/s^2 and the block's acceleration has a magnitude of 450 m/s^2.
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?

Homework Equations


I tried doing a= v/t. to find the time. but the answer wasnt right. i really don't know where to start for it.

The Attempt at a Solution


I need help on parts a and b. i really have no ideas what to do.
 
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i just need a formula to get going.
 
For arrow, v= u -a1*t. For block, v = 0 + a2*t. You find v and t. Enough?
 

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