Question

A particle is projected at 30° with a velocity of 20 m/s. What is the maximum height it reaches?

Answer 1

5 m

Answer 2

The maximum height reached by a projectile is given by the formula:

$H = \frac{u^2 \sin^2 \theta}{2g}$

where:
$u$ = initial velocity of projection
$\theta$ = angle of projection with the horizontal
$g$ = acceleration due to gravity

Given values:
Initial velocity, $u = 20$ m/s
Angle of projection, $\theta = 30^\circ$
Acceleration due to gravity, $g = 10$ m/s$^2$

First, calculate $\sin \theta$:
$\sin 30^\circ = \frac{1}{2} = 0.5$

Now, substitute the values into the formula:
$H = \frac{(20)^2 \times (0.5)^2}{2 \times 10} = \frac{400 \times 0.25}{20} = \frac{100}{20} = 5 \text{ m}$

The maximum height reached by the particle is 5 meters.