Answer to Question #141312 in Physics for Sydney

Question

In yet another crash safety test, a 2550 kg truck traveling east at 19.5 m/s crashes into a 178- kg compact car that is traveling north at 39.2 m/s. The two crumple together and travel as one unit. Find their velocity (magnitude and direction) after the collision.

Answer 1

To solve this problem, we will apply law of conservation of momentum and energy.

Momentum along east and north direction: initial = final. Initially, they traveled as separate objects in perpendicular directions. Finally, they both travel as one body with two components of velocity along x- and y-axis.

$$Mv_x=(m+M)u_x,\\ mv_y =(m+M)u_y.\\\space\\ u_x=v_x\frac{M}{m+M},\\\\\space\\ u_y=v_y\frac{m}{m+M},\\\\\space\\ u=\sqrt{u_x^2+u_y^2}=\frac{\sqrt{M^2v_x^2+m^2v_y^2}}{m+M}=18.41\text{ m/s}.$$

$$\theta=\text{atan}\bigg(\frac{u_y}{u_x}\bigg)=\text{atan}\bigg(\frac{v_ym}{v_xM}\bigg)=8.11°.$$

The angle is counted from east direction toward north.