Final answer:
To rise 0.750 m above the floor, the basketball player needs a vertical velocity of approximately 8 m/s. To reach his maximum height at the same time as he reaches the basket, the player must start his jump approximately 8 meters away from the basket in the horizontal direction.
Step-by-step explanation:
To rise 0.750 m above the floor, the basketball player needs a vertical velocity. Since the player maintains his horizontal velocity, the vertical and horizontal motions are independent of each other.
Using the formula vf = vi + gt, where vf is the final velocity, vi is the initial velocity, g is the acceleration due to gravity, and t is the time taken, we can calculate the required vertical velocity.
Setting vi to 0 m/s (as the player starts from rest), g to 9.8 m/s², and solving the equation for vf and t, we find that the vertical velocity needed is approximately 8 m/s.
To calculate how far the player must start his jump from the basket to reach his maximum height at the same time as he reaches the basket, we can use the formula d = vt, where d is the distance traveled, v is the velocity, and t is the time taken.
Since the player maintains his horizontal velocity, the time taken for him to reach the basket is the same as the time taken for him to reach his maximum height.
Therefore, we can use the vertical velocity calculated in part (a) as v in the formula. Setting d to 0 m (as the player starts from the basket), and solving the equation for t, we find that the player must start his jump approximately 8 meters away from the basket in the horizontal direction.