Question

Two automobiles traveling at right angles to each other collide and stick together. Car a has a mass of 1200 kg and had a speed of 25 m/s before the collision. Car b has a mass of 1600 kg. The skid marks show that, immediately after the collision, the wreckage was moving in a direction making an angle of 40 with the original direction of car
a. What was the speed of car b before the collision, assuming that any other unbalanced forces are negligible?

Answer 1

The speed of car b before collision is 15.72 m/s.

Explanation:

Given that,

Mass of car a= 1200 kg

Speed = 25 m/s

Mass of car b = 1600 kg

Angle = 40

We need to calculate the speed of car b before the collision

Using conservation of momentum

Horizontal momentum,

$P_{i}=P_{f}$

$m_{1}v_{1}=(m_{1}+m_{2})\times v\cos\theta$

Put the value into the formula

$1200\times25=(1200+1600)v\times\cos40$

$v=\dfrac{1200\times25}{2800\times\cos40}$

$v=13.98\ m/s$

Vertical momentum,

$P_{i}=P_{f}$

$m_{2}v_{2}=(m_{1}+m_{2})\times v\sin\theta$

Put the value into the formula

$1600\times v=(1200+1600)\times13.98\times\sin40$

$v_{2}=\dfrac{2800\times13.98\sin40}{1600}$

$v_{2}=15.72\ m/s$

Hence, The speed of car b before collision is 15.72 m/s.

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Topic : collision

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