A soccer ball is kicked from the ground with an initial speed of 20.0 m/s at an upward angle of 43.7˚. A player 50.3 m away in the direction of the kick starts running to meet the ball at that instant. What must be his average speed if he is to meet the ball just before it hits the ground? Neglect air resistance.

Question

A soccer ball is kicked from the ground with an initial speed of 20.0 m/s at an upward angle of 43.7˚. A player 50.3 m away in the direction of the kick starts running to meet the ball at that instant. What must be his average speed if he is to meet the ball just before it hits the ground? Neglect air resistance.

Answer 1

To solve this problem, we need to analyze the motion of the soccer ball and the player separately, and then find the required average speed of the player.

First, let's analyze the motion of the soccer ball. We can separate its initial velocity into horizontal and vertical components. The vertical component can be found using the angle of 43.7˚:

Initial vertical velocity (Vy) = Initial speed × sin(angle)
= 20.0 m/s × sin(43.7˚)

The horizontal component of the velocity remains constant throughout the motion since air resistance is neglected.

Now, let's calculate the time it takes for the soccer ball to hit the ground. We can use the equation for vertical motion:

Vertical displacement (h) = (Initial vertical velocity × time) - (0.5 × g × time²)
where g is the acceleration due to gravity (approximately 9.8 m/s²)

Since the soccer ball is projected upwards, at the point where it hits the ground, its vertical displacement is equal to zero. We can set up the equation:

0 = (Initial vertical velocity × time) - (0.5 × g × time²)

Solving this equation for time will give us the time it takes for the ball to reach the ground.

Now, let's analyze the motion of the player. The player is 50.3 m away from the starting point of the ball at the instant it is kicked. The player starts running at that instant with an unknown average speed. The time required for the player to meet the ball is the same as the time calculated for the ball to hit the ground.

Finally, we can find the average speed of the player by dividing the total distance traveled by the player by the time taken:

Average speed = Total distance / Time
= 50.3 m / (calculated time)

By following these steps and calculating the required time, you can find the average speed of the player needed to meet the ball just before it hits the ground.