Final answer:
A basketball player needs to leave the ground at an initial velocity of approximately 4.95 m/s to reach a height of 1.25 m above the floor to intercept a basketball during the tip-off.
Step-by-step explanation:
When considering the action of a basketball player jumping to reach a ball tossed up by the referee during the tip-off, we can use kinematic equations to determine the initial velocity required. We'll apply the kinematic equation for vertical motion without air resistance:
v2 = u2 + 2gh,
where
- v is the final velocity (0 m/s at the top of the jump),
- u is the initial velocity,
- g is the acceleration due to gravity (approximately 9.81 m/s2), and
- h is the height of the jump (1.25 m).
Rearranging the equation to solve for u gives:
u = sqrt(2gh).
Plugging in the values gives:
u = sqrt(2 * 9.81 m/s2 * 1.25 m).
After calculation, we find that the initial velocity u should be approximately 4.95 m/s. Therefore, the basketball player needs to leave the ground at an initial velocity of about 4.95 meters per second to rise 1.25 meters above the floor in an attempt to get the ball.