Question

A soccer player kicks the ball in a parabolic path. The ball leaves the player's foot with a speed of 23.0 m/s, making an angle of 30.0º with the horizontal. At what distance from the soccer player does the ball reach its maximum height (use g = 9.81 m/s2 ?

Answer 1

The distance from the soccer player where the ball reaches its maximum height is approximately 6.37 meters.

Step-by-step explanation:

To find the distance from the soccer player where the ball reaches its maximum height, we can use the equation for the maximum height of a projectile. The maximum height occurs when the vertical component of the velocity becomes zero. In this case, the initial vertical velocity is given by 23.0 m/s * sin(30.0°) = 11.5 m/s. Using the equation v^2 = u^2 + 2as, where v = 0, u = 11.5 m/s, and a = -9.81 m/s^2 (acceleration due to gravity), we can solve for s to find the maximum height.

The equation becomes: 0 = (11.5 m/s)^2 + 2(-9.81 m/s^2)s. Solving for s, we find that the ball reaches its maximum height at s = 6.37 m. Therefore, the distance from the soccer player where the ball reaches its maximum height is approximately 6.37 meters.