Question

A stone is projected vertically upwards with speed 'v'. Another stone of same mass is projected at an angle of $60^\circ$ with the vertical with the same speed 'v'. The ratio of their potential energies at the highest points of their journey is [$\sin 30^\circ = \cos 60^\circ = 0.5$, $\cos 30^\circ = \sin 60^\circ = \frac{\sqrt{3{2}$]

• A. 4:1
• B. 2:1
• C. 3:2
• D. 1:1

Hint:

Logic Tip: The potential energy at the highest point is determined exclusively by the vertical component of the launch velocity ($v_y = v \sin\theta$). Since $PE \propto v_y^2$, the ratio is simply $\frac{(v \sin 90^\circ)^2}{(v \sin 30^\circ)^2} = \frac{1^2}{0.5^2} = \frac{1}{0.25} = 4$.

Answer 1

The Correct Option is A