Question

A ball thrown at an angle of 30° with the horizontal strikes the ground five seconds later. How far from the starting point does it hit the ground?​

Answer 1

Given :

Angle of projection = 30°

Time of flight = 5s

To Find :

Range of projectile.

Solution :

❖ A body is said to be projectile if it is projected into space with some initial velocity and then it continues to move in a vertical plane such that its horizontal acceleration is zero and vertical downward acceleration is equal to g.

First of all we need to find initial velocity of ball.

A] Time of flight :

$\sf:\implies\:T=\dfrac{2u \:sin\theta}{g}$

$\sf:\implies\:5=\dfrac{2u \:sin30^{\circ}}{10}$

$\sf:\implies\:25=u\times\dfrac{1}{2}$

$\bf:\implies\:u=50\:ms^{-1}$

B] Range of projectile :

$\sf:\implies\:R=\dfrac{u^2\:sin2\theta}{g}$

$\sf:\implies\:R=\dfrac{(50)^2\:sin2(30^{\circ})}{10}$

$\sf:\implies\:R=\dfrac{2500\times sin60^{\circ}}{10}$

$\sf:\implies\:R=250\times\dfrac{\sqrt3}{2}$

$\sf:\implies\:R=\dfrac{432.5}{2}$

$:\implies\:\underline{\boxed{\bf{\red{R=216.25\:m}}}}$