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

A. 65 degrees

Step-by-step explanation:

The formula to calculate the range of a projectile is:

`d=(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:

`(u^2 sin (2\cdot 25^(\circ)))/(g)=(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)`