Question

A soccer player kicks a ball at an angle of 60∘60∘ above the ground. The soccer ball hits the ground some distance away. Neglect any effects due to air resistance. Is there any point at which the soccer ball's velocity and acceleration vectors are perpendicular to each other? No, because the change in velocity vector and the acceleration vector point in the same direction at every point along the trajectory. Yes, because at the highest position in the trajectory, the velocity vector points horizontally, and the acceleration vector points vertically downward. No, because the vertical component of the velocity vector points in the same direction as the acceleration vector at all times. Yes, because the velocity vector is always tangent to the trajectory’s curve, and the acceleration vector always points toward the center of curvature.

Answer 1

Answer:

Yes, because at the highest position in the trajectory, the velocity vector points horizontally, and the acceleration vector points vertically downward.

Explanation:

The motion of the ball is a projectile motion, which consists of two independent motions:

- A horizontal motion with constant velocity

- A vertical motion with constant downward acceleration (acceleration of gravity)

While the horizontal component of the velocity is constant, the vertical velocity constantly changes. In particular, it starts with a certain value $u_y$ (with upward direction), then decreases until the ball reaches its maximum height along the trajectory (at this point, the vertical velocity is zero), and then it starts to increase again in magnitude (but having changed direction, now downward) as the ball falls down.

Therefore, at the maximum height the velocity vector points horizontally. Instead, the acceleration always points downward during the whole motion (because gravity, downward, is the only force acting on the ball): so the two vectors are perpendicular when the ball reaches the maximum height, and therefore, the statement

Yes, because at the highest position in the trajectory, the velocity vector points horizontally, and the acceleration vector points vertically downward.

is true.