Abasketball player is running at 5.00 m/s directly toward the basket when he jumps into the air to dunk the ball. he maintains his horizontal velocity. (a) what vertical velocity does he need to rise 0.750 m above the floor? (b) how far from the basket (measured in the horizontal direction) must he start his jump to reach his maximum height at the same time as he reaches the basket?

1.95m

Explanation:

To calculate the vertical velocity needed we use the formula , where we will take the upwards direction as the positive one (gravity will be negative). We will use it only for the vertical component, and we know that at maximum height the final vertical velocity must be 0m/s, so the initial velocity to achieve that displacement must be:

How far in the horizontal direction must be calculated with the formula since there is no acceleration in that component, but we need the time he needed to do it. We will obtain it using the equation, and looking at the vertical component again (since time will be the same for both components, something obvious but powerful):

We can substitute this on the previous equation:

And using our values we get:

force is mass*acceleration.

we have a very small mass: 11.4*0.001 kg

if we want 0.035n of force, we need an acceleration:

0.035 = 11.4*0.001*a

a = 0.035/(11.4*0.001) m/s^2