Question

Two cars, one of mass 1100 kg, and the second of mass 2500 kg, are moving at right angles to each other when they collide and stick together. The initial velocity of the first car is 14 m/s in the positive x direction and that of the second car is 19 m/s in the positive y direction. What is the magnitude of the velocity of the wreckage of the two cars immediately after the collision?

Answer 1

Answer:

$v_{f}=17.47 m/s$

Explanation:

Let's use the conservation of momentum to solve it.

$p_{initial}= p_{final}$ (1)

• The total initial momentum will be: $m_{1}v_{1i}+m_{2}v_{2i}$
• The total final momentum will be: $m_{1}v_{1f}+m_{2}v_{2f}$, but as they stick together after the collision, v1f = v2f = vf.

So we can rewrite (1), using the above information:

$m_{1}v_{1i}+m_{2}v_{2i}=m_{1}v_{f}+m_{2}v_{f}$

$m_{1}v_{1i}+m_{2}v_{2i}=v_{f}(m_{1}+m_{2})$

$v_{f}=\frac{m_{1}v_{1i}+m_{2}v_{2i}}{m_{1}+m_{2}}$

$v_{f}=\frac{1100\cdot 14+2500\cdot 19}{1100+2500}$

Finally, the magnitude of the velocity of the wreckage of the two cars immediately after the collision is:

$v_{f}=17.47 m/s$

I hope it helps you!