Two cars of same mass are moving with same speed $v$ on two different roads inclined at an angle $θ$ with each other, as shown in the figure. At the junction of these roads the two cars collide in elastically and move simultaneously with the same speed. Find the speed of these cars.

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Solution

Applying law of conservation of momentum along horizontal axis.
$m v cos θ / 2 + m v cos / 2 = m v_{2} + m v_{2} \Rightarrow 2 v cos θ / 2 = 2 v_{2}$
$∴$ Final velocity $v_{2} = v cos θ / 2$

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Two cars of same mass are moving with same speed v on two different roads inclined at an angle θ with each other, as shown in the figure. At the junction of these roads the two cars collide in elastically and move simultaneously with the same speed. Find the speed of these cars.

Applying law of conservation of momentum along horizontal axis.mvcosθ/2+mvcos/2=mv2+mv2⇒2vcosθ/2=2v2∴ Final velocity v2=vcosθ/2

Two cars of same mass are moving with same speed $v$ on two different roads inclined at an angle $θ$ with each other, as shown in the figure. At the junction of these roads the two cars collide in elastically and move simultaneously with the same speed. Find the speed of these cars.

Applying law of conservation of momentum along horizontal axis.
$m v cos θ / 2 + m v cos / 2 = m v_{2} + m v_{2} \Rightarrow 2 v cos θ / 2 = 2 v_{2}$
$∴$ Final velocity $v_{2} = v cos θ / 2$