Question

A 1500-kg car traveling east with a speed of 25.0 m/s collides at an intersection with a 2500-kg van traveling north at a speed of 20.0 m/s. Find the direction and magnitude of the velocity of the wreckage after the collision, assuming that the vehicles undergo a perfectly inelastic collision (i.e. they stick together).

Answer 1

Answer:

The direction and magnitude of velocity is 38.65° and 12.005 m/s

Explanation:

Given that,

Mass of car = 1500 kg

Speed of car = 25.0 m/s

Mass of van = 2500 kg

Speed of van =20.0 m/s

We need to calculate the velocity

Using conservation of energy

$m_{c}u_{i}+m_{v}u_{i}=(m_{c}+m_{v})v_{f}$

$1500(25i+0j)+2500(0+20j)=4000(v_{f})$

$v_{f}=\dfrac{1500\times25}{4000}i+\dfrac{1500\times20}{4000}j$

$v_{f}=9.375 i+7.5 j$

The magnitude of velocity

$|v_{f}|=\sqrt{(9.375)^2+(7.5)^2}$

$|v_{f}|=12.005\ m/s$

We need to calculate the direction

$\tan\theta=\dfrac{coefficient\ of\ j}{coefficient\ of\ i}$

$\tan\theta=\dfrac{7.5}{9.375}$

$\theta=\tan^{-1}0.8$

$\theta=38.65^{\circ}$

Hence, The direction and magnitude of velocity is 38.65° and 12.005 m/s.