Question

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

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

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 $v=20\text{m/s}$.
Since the resultant displacement along horizontal is zero.

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