Question

A member of the Penn State Women's Basketball team performs a jumping movement simulating that used in a jump shot. The time from take-off to landing (total time) is measured to be 0.8 seconds. Compute the following,
a) The vertical displacement of her center of mass (height of jump) Vertical Displacement of Center of Mass = __________

b) Her initial vertical velocity at the instant of takeoff. Initial Velocity at takeoff = __________

Answer 1

A) Starting from rest, we have the entire cycle determined by 0.8s.

If we assume a constant movement, half of that time is when it reaches the highest point, that is, in 0.4s.

The distance as a function of speed and acceleration is given by,

$d=v_it+\frac{1}{2}at^2$

At the initial point the speed is zero and the acceleration is equivalent to gravity.

$d= 0+ \frac{1}{2}9.8*0.4^2$

$d=0.784m$

B) When returning to the ground, the final speed is zero. Therefore, the equation that relates velocity to acceleration is given by,

$V_f = V_i+at$

$0 = V_i -9.8(0.4)$

$V_i = 3.92m/s$