Question

Two cars, one of mass 1300 kg, and the second of mass 2400 kg, are moving at right angles to each other when they collide and stick together. The initial velocity of the first car is 12 m/s in the positive x direction and that of the second car is 18 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

To solve this problem we will apply the momentum conservation theorem, that is, the initial momentum of the bodies must be the same final momentum of the bodies. The value that will be obtained will be a vector value of the final speed of which the magnitude will be found later. Our values are given as,

$m_1 = 1300kg$

$m_2 = 2400kg$

$u_1 = 12m/s i$

$u_2 = 18m/s j$

Using conservation of momentum,

$m_1u_1+m_2u_2 = (m_1+m_2)v_f$

$1300*12i-2400*18j = (1300+2400)v_f$

Solving for $v_f$

$v_f = 4.2162i-11.6756j$

Using the properties of vectors to find the magnitude we have,

$|v| = \sqrt{(4.2162^2)+(-11.6756)^2}$

$|v| = 12.4135m/s$

Therefore the magnitude of the velocity of the wreckage of the two cars immediately after the collision is 12.4135m/s