Projectile and Box


A 0.15 kg projectile hits a 1.5 kg box that is initially at rest. The projectile imbeds itself in the box, and then they both slide forward and up a slope. How far up the slope do they go? Assume a smooth transition between the slopes and no friction.



Motion of Projectile and Box


This is a two step problem. The velocity of the combined projectile and box needs to be determined before the distance s can be calculated.

Velocity of box and projectile after impact

     mboxvbox + mprojvproj = (mbox + mproj) v2
     1.5 (0) + 0.15 (25) = (1.5 + 0.15) v2
     v2 = 2.273 m/s

The distance the box travels up the slope can be determined using either line motion or energy concepts. Using the conservation of energy (kinetic and gravity), gives

     Vk2 + Tg2 = Vk3 + Tg3
     0.5mv22 + mgh2 = 0.5mv32 + mgh3
     0.5(1.5 + 0.15)(2.273)2 + 0
           = 0 + s sin15 (9.81)(1.5 + 0.15)

s = 1.017 m

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