A projectile is fired at an angle of elevation of 60 $\degree$.Neglecting air resistance,what are possible angles in flight between the acceleration vector and the velocity vector?
A)160 $\degree$ and 40 $\degree$
B)20 $\degree$ and 70 $\degree$
C)90 $\degree$ and 60 $\degree$
D)none of the above

Question

Quizplus · Accepted Answer

When a projectile is fired at an angle of elevation, the acceleration vector (due to gravity) is always straight down towards the ground. The only variable is the direction of the velocity vector.

At the top of the projectile's trajectory, the velocity vector is perpendicular to the acceleration vector, so the angle between them is 90 degrees. As the projectile begins to fall back towards the ground, the angle between the velocity and acceleration vectors decreases.

Since the angle of elevation in this problem is 60 degrees, the initial velocity vector is also 60 degrees above the horizontal. Therefore, at the top of the trajectory, the velocity vector is pointing straight up and the angle between the velocity and acceleration vectors is 90 degrees.

As the projectile continues to fall, the angle between the velocity and acceleration vectors decreases. However, the only answer choice that includes 90 degrees as a possibility is C. Therefore, C is the best choice.

A Projectile Is Fired at an Angle of Elevation of 60