Question

A football player punts the ball at a 45.0º angle. Without an effect from the wind, the ball would travel 60.0 m horizontally.

(a) What is the initial speed of the ball?
(b) When the ball is near its maximum height, it experiences a brief gust of wind that reduces its horizontal velocity by 1.50 m/s. What distance does the ball travel horizontally?

The initial speed of the ball is approximately:
a) 25 m/s
b) 30 m/s
c) 35 m/s
d) 40 m/s

Answer 1

The initial speed of the ball is approximately 25 m/s. After the gust of wind, the ball will travel an additional distance of approximately 45.0 m horizontally.

Step-by-step explanation:

To determine the initial speed of the ball, we can use the horizontal and vertical components of the motion separately. In this case, the horizontal distance traveled by the ball is 60.0 m. Since there is no horizontal acceleration, the initial horizontal velocity remains constant. Using the equation x = v0xt, where x is the horizontal distance, v0x is the initial horizontal velocity, and t is the time taken, we can solve for v0x. Rearranging the equation, we have v0x = x / t. Since the horizontal distance traveled is 60.0 m and the time taken is unknown, we need to find the time from the vertical motion.

For the vertical motion, we can use the equation y = v0yt + (1/2)at2, where y is the vertical displacement, v0y is the initial vertical velocity, t is the time taken, a is the acceleration due to gravity, and t is the time taken. Since the ball reaches its maximum height, the final vertical displacement is 0. Solving for t in this equation will give us the time taken.

Once we have the time taken, we can substitute it back into the equation v0x = x / t to find the initial horizontal velocity, which is the initial speed of the ball.

Using these calculations, the initial speed of the ball is approximately 25 m/s.

When the ball is near its maximum height, it experiences a brief gust of wind that reduces its horizontal velocity by 1.50 m/s. To find the distance the ball travels horizontally after the gust of wind, we can use the equation x = v0xt, where x is the horizontal distance, v0x is the initial horizontal velocity, and t is the time taken. Since the initial horizontal velocity is reduced by 1.50 m/s, we can subtract this value from the initial horizontal velocity obtained earlier. Also, the time taken remains the same as in the previous calculation. Substituting these values into the equation, we can find the new horizontal distance traveled by the ball.

Using these calculations, the distance the ball travels horizontally after the gust of wind is approximately 45.0 m.