Question

A ball is thrown with a velocity of 40 m/s at an angle of 30° above the horizontal and attains a certain range R. At what other angle will this ball attain the same range keeping its initial velocity the same?

Answer 1

Answer:

This ball will attain the same range at 60°.

Explanation:

Projectile motion: when an object is thrown in such a way that it form an angle with horizon, the force act on it that is the acceleration due gravity. This type of motion is known as projectile motion.

Range: The horizontal distance is covered by an object.

Range $=\frac{u^2 sin2\theta}{g}$

u = initial velocity = 40 m/s

θ = 30°

g = gravity =9.8 m/s²

$Range=\frac{40^2\times sin(2\times 30^\circ)}{9.8}$

         $=\frac{800\sqrt{3} }{9.8}$

Next,

Range $=\frac{800\sqrt{3} }{9.8}$ and u = 40 m/s

$sin2\theta =\frac{Range \times g}{u^2}$

$\Rightarrow sin2\theta =\frac{\frac{800\sqrt{3} }{9.8} \times 9.8}{40^2}$

$\Rightarrow sin 2\theta =\frac{\sqrt{3} }{2}$

$\Rightarrow sin 2\theta = sin 120^\circ$

$\Rightarrow \theta =120^\circ$

$\Rightarrow \theta =60^\circ$

This ball will attain the same range at 60°.