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Alenkinab [10]
2 years ago
5

Two cars, both of mass m, collide and stick together. Prior to the collision, one car had been traveling north at a speed 2v, wh

ile the second was traveling in a southeastern direction at an angle ϕ with respect to the east-west direction and at a speed v. After the collision, the two-car system travels in a northeastern direction at an angle θ with respect to the north-south direction and at a speed vfinal.
Find v_final, the speed of the joined cars after the collision.

Physics
1 answer:
mel-nik [20]2 years ago
7 0

Answer:u=\frac{v}{2}\sqrt{5-4sin\phi }

Explanation:

Given

Both cars mass is m

and solving problem in Vertical and horizontal direction

considering + y and +x to be positive and u be the final velocity of system

Conserving Momentum in Vertical direction

m(2v)+m(-vsin\phi )=2m(ucos\theta )

2ucos\theta =v(2-sin\theta )------1

Conserving momentum in x direction

mvcos\phi =2musin\theta-----2

squaring and adding 1 &2

(2u)^2=(2v-vsin\phi )^2+(vcos\phi )^2

4u^2=4v^2+v^2-4v^2sin\phi

4u^2=5v^2-4v^2sin\phi

u=\frac{v}{2}\sqrt{5-4sin\phi }

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