Question

A cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same effort, he throws the ball vertically upwards. What is the maximum height attained by the ball?

• A. 50 m
• B. 60 m
• C. 70 m
• D. 80 m

Answer 1

The correct option is A

50 m

For maximum range, the angle of projection is ${45}^{\circ }$.
$R_{max}=\frac{v_0^{2}sin2\theta }{g}=\frac{v_0^{2}sin{90}^{\circ }}{g}=\frac{v_0^2}{g}........\left(1\right)$
When thrown vertically upwards, the angle of projection is ${90}^{\circ }$ and the maximum height reached is given by
$h_{max}=\frac{v_0^{2}si{n}^2\theta }{2g}=\frac{v_0^{2}si{n}^2{90}^{\circ }}{2g}=\frac{v_0^2}{2g}........\left(2\right)$
Comparing equations (1) and (2), we get $h_{max}=\frac{R_{max}}{2}=\frac{100m}{2}=50m$. Hence the correct choice is (a).