Question

A truck is moving with a constant velocity of $54\, km/h$. In which direction (angle with the direction of motion of track) should a stone be projected up with a velocity of $20 \,m/s$, from the floor of the truck, so as to appear at right angles to the truck, for a person standing on the earth ?

• A. $\cos ^{-1}\left(-\frac{3}{4}\right)$
• B. $\cos ^{-1}\left(-\frac{1}{4}\right)$
• C. $\cos ^{-1}\left(-\frac{2}{3}\right)$
• D. $\cos ^{-1}\left(\frac{3}{4}\right)$

Answer 1

Answer: (A)

Let the stone be projected at an angle α to the direction of motion of truck with a speed of v = 20 m/s.
Since the resultant displacement along horizontal is zero.

The velocity along horizontal $=0$ $15+20 \cos \alpha=0 \quad \Rightarrow \quad \cos \alpha=-\frac{3}{4}$
$\Rightarrow \quad \alpha=\cos ^{-1}\left(-\frac{3}{4}\right)$