Question

A ball is projected at 45°, its horizontal range is 10m, the height attained by the projectile is?

a) 2m b) 4m c) 3m d) 2.5m

Answer 1

Given:

Angle of projectile $\sf (\theta)$ = 45°

Horizontal Range (R) = 10 m

To Find:

Height attained by the projectile (H)

Answer:

Relation between Horizontal Range, Maximum Height and Angle of Projectile:

$\boxed{ \bf{tan \theta = \dfrac{4H}{R}}}$

By substituting values, we get:

$\rm \leadsto tan \theta = \dfrac{4H}{R} \\ \\ \rm \leadsto tan {45}^{ \circ} = \dfrac{4H}{10} \\ \\ \rm \leadsto 1 = \dfrac{4H}{10} \\ \\ \rm \leadsto H = \dfrac{10}{4} \\ \\ \rm \leadsto H = 2.5 \: m$

$\therefore$ Height attained by the projectile (H) = 2.5 m

Correct Option: (d) 2.5 m