A car is moving at a velocity of 8 km/hour. A body is thrown outside the car at a velocity of 16 km/hour. If the body moves perpendicular to the car, what is the angle at which the body was thrown ?

Question

A car is moving at a velocity of 8 km/hour.  A body is thrown outside the car at a velocity of 16 km/hour. If the body moves perpendicular to the car,  what is the angle at which the body was thrown ?

Accepted Answer

গ. 120°

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Let the car velocity be along the $x$-axis: $\vec{v}_c = 8\hat{i}$. The body is thrown with velocity $v_b$ relative to the ground (or car). Usually, in such classic problems, the velocity relative to the car is thrown at an angle, or velocity $v = 16\ 	ext{km/h}$ is thrown relative to the car/ground. Standard mechanics question: If velocity of car is $u = 8$, thrown velocity $v = 16$ at angle $\alpha$ with the direction of motion such that the resultant velocity $R$ is perpendicular to the car's direction: $R = u + v\cos\alpha = 0 \Rightarrow \cos\alpha = -\frac{u}{v} = -\frac{8}{16} = -\frac{1}{2} \Rightarrow \alpha = 120^\circ$.

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