Answer:
A. 65 degrees
Explanation:
The formula to calculate the range of a projectile is:
[tex]d=\frac{u^2 sin (2\theta)}{g}[/tex]
where
u is the initial speed of the projectile
g is the acceleration of gravity
[tex]\theta[/tex] is the angle of projection of the projectile
We want to find the angle [tex]\theta'[/tex] such that it has the same range of a projectile fired at [tex]25^{\circ}[/tex], therefore:
[tex]\frac{u^2 sin (2\cdot 25^{\circ})}{g}=\frac{u^2 sin (2\theta')}{g}[/tex]
It follows that
[tex]sin(2\theta') = sin(50^{\circ})[/tex]
And there are two angles that satisfies this condition:
[tex]\theta' = 25^{\circ}[/tex]
and
[tex]\theta' = 65^{\circ}[/tex]
In fact, with the second choice,
[tex]sin (2\cdot 65^{\circ})=sin (130^{\circ}) = sin(50^{\circ}[/tex]
