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**1. Homework Statement**

Mr. Gale decides to build his own velocity measuring machine.

His plan is to build a box (mass 2.50 kg) that catches the ball (mass 0.500 kg) being thrown. It then slides across the desk but eventually comes to a stop due to friction (μ = 0.800) between the box and the surface. He thinks that knowing how far the box slides will allow him to calculate the velocity of the ball just before it hits the box. To test this out he throws the ball and the box slides exactly 38 centimeters. Calculate how fast the ball must have been going just before it hit the box.

**3. The Attempt at a Solution**

There were two different ways to approach it. But this gave different answers. One of these is wrong.

ATTEMPT 1 : Using Energy

KE of the ball before just before it hits the box = Work done by friction on the box and ball combined

0.5(0.5kg)v^2 = (0.800)(2.50 + 0.5)(9.8)(0.38)

v = 6.0 m/s

ATTEMPT 2 : Using Force and Momentum

friction is net force, calculate velocity, use momentum to calculate initial velocity in ball

f = (2.50 + 0.5)(9.8)(0.800) = 23.52 = ma

therefore a = (23.52)/(2.50 + 0.5) = 7.84 m/s^2

using v^2 = 2ad

v = sqrt((2)(7.84)(.38)) = 2.44 m/s

therefore pi = pf

(0.5)(v) = (2.44)(2.50 + 0.5)

v = 14.64 m/s

why am I getting different values? There is something I am forgetting here.

Thanks for any help in advance