Question

A projectile fired at 25 degrees will have the same range as a projectile fired at ____ angle. A. 65 degrees B. 35 degrees C. 45 degrees D. 75 degrees

Answer 1

Answer:

A. 65 degrees

Explanation:

The formula to calculate the range of a projectile is:

$d=\frac{u^2 sin (2\theta)}{g}$

where

u is the initial speed of the projectile

g is the acceleration of gravity

$\theta$ is the angle of projection of the projectile

We want to find the angle $\theta'$ such that it has the same range of a projectile fired at $25^{\circ}$, therefore:

$\frac{u^2 sin (2\cdot 25^{\circ})}{g}=\frac{u^2 sin (2\theta')}{g}$

It follows that

$sin(2\theta') = sin(50^{\circ})$

And there are two angles that satisfies this condition:

$\theta' = 25^{\circ}$

and

$\theta' = 65^{\circ}$

In fact, with the second choice,

$sin (2\cdot 65^{\circ})=sin (130^{\circ}) = sin(50^{\circ}$