Question

During a high school football game, a field goal is attempted from just outside the thirty yard line. The total distance from the ball to the goal posts is 40 meters. The crossbar of the goal posts is 7.3 m high. To be good, a field goal attempt must pass over the crossbar. The velocity of the ball after being kicked is 25 m/s at an angle of 37° above the horizontal. Determine the ball's velocity at its highest point.

Answer 1

The velocity of the ball at its highest point in a field goal attempt is equal to its initial horizontal velocity, which can be found by multiplying the initial velocity by the cosine of the angle of projection.

Step-by-step explanation:

The question asks us to determine the ball's velocity at its highest point during a football field goal attempt. At the highest point of its trajectory, the vertical component of the ball's velocity will be 0 m/s because gravity will have decelerated the ball's vertical motion to a momentary halt before it starts to fall back down. However, the horizontal component of the velocity remains unchanged (assuming no air resistance), as there are no forces acting in the horizontal direction once the ball is in flight.

To find the horizontal component of velocity, we use the initial velocity and the angle of projection:

Horizontal velocity (vx) = Initial velocity (v) × cos(θ)

Given that the initial velocity (v) is 25 m/s and the angle of projection (θ) is 37°:

vx = 25 m/s × cos(37°)

vx is thus the ball's velocity at its highest point. However, we would need to calculate this value using a calculator to find the numerical answer.