Question

a basketball player can leap upward .65m how long does the basketball player remain in the air use 9.81m/s²​

Answer 1

At the player's maximum height, their velocity is 0. Recall that

${v_f}^2-{v_i}^2=2a\Delta y$

which tells us the player's initial velocity $v_i$ is

$0^2-{v_i}^2=-2g(0.65\,\mathrm m)\implies v_i=3.6\dfrac{\rm m}{\rm s}$

The player's height at time $t$ is given by

$y=v_it-\dfrac g2t^2$

so we find their airtime to be

$0.65\,\mathrm m=\left(3.6\dfrac{\rm m}{\rm s}\right)t-\dfrac g2t^2\implies t=0.36\,\mathrm s$