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

     m_boxv_box + m_projv_proj = (m_box + m_proj) 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

     V_k2 + T_g2 = V_k3 + T_g3
     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