A missile is fired for maximum range with an initial velocity of $20\, m/s$. If $g = 10 \,m/s^2$, the range of the missile is

Question

A ball is thrown vertically upwards with an initial velocity of $ 20 \, \text{m/s} $. How high will the ball rise? (Take $ g = 10 \, \text{m/s}^2 $)

Answer 1

To solve this problem, we need to determine the maximum range of a projectile (missile) when fired with a given initial velocity. The formula for the range (R) of a projectile fired at an angle (\theta) with an initial velocity (u) is given by:

R = \dfrac{u^2 \sin(2\theta)}{g}

For maximum range, the angle of projection should be 45^\circ, meaning 2\theta = 90^\circ, hence \sin(90^\circ) = 1.

Given:

Initial velocity (u) = 20 \, m/s
Acceleration due to gravity (g) = 10 \, m/s^2

Substituting the values in the formula:

R = \dfrac{(20)^2 \times 1}{10}

Calculating further:

R = \dfrac{400}{10} = 40 \, m

Therefore, the range of the missile is 40 m, making the correct answer: 40 m.

Answer 2