Question

A truck is moving with a constant velocity of $54km{h}^{-1}$. In which direction (angle with the direction of motion of truck) should a stone be projected up with a velocity of $20m{s}^{-1}$, from the floor of the truck, so as to appear at right angles to the truck, for a person standing on earth?

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

Answer 1

The correct option is A ${\cos }^{-1}(-\frac{3}{4})$

Let the stone be projected at an angle $\alpha$ to the direction of motion of truck with a speed of $v=20m{s}^{-1}$.

Since the resultant displacement along horizontal is zero, the velocity along horizontal is $0$

$15+20\cos \alpha =0$

$\Rightarrow \cos \alpha =-\frac{3}{4}$

$\Rightarrow \alpha ={\cos }^{-1}(-\frac{3}{4})={138}^o{35}^{\prime }$