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?
A) 15°
B) 90°
C) 120°
D) 60°
E) All other angles will give different ranges.

Question

Quizplus · Accepted Answer

The range of a projectile launched with a velocity v at an angle θ above the horizontal is given by:

R = (v^2/g)sin(2θ)

where g is the acceleration due to gravity.

For the given scenario, the range is R = (40^2/9.8)sin(60) = 400 m.

To find the angle at which the ball will attain the same range, we need to solve the above equation for θ:

sin(2θ) = Rg/v^2

θ = (1/2)sin^-1(Rg/v^2)

Plugging in the values, we get:

θ = (1/2)sin^-1(400x9.8/40^2) = 60°

Therefore, the ball will attain the same range at an angle of 60° above the horizontal. Choice D is the correct answer.

A Ball Is Thrown with a Velocity of 40 M/s