# Math Help - Finding Velocity, time, distance

1. ## Finding Velocity, time, distance

An Olympic long jumper jumps 8.04m, reaching a height of 0.80 m halfway through his jump. What was his velocity as he left the ground? Also, how far would he be able to jump on the moon (g=1.63 N/kg) and how much time would he spend off the lunar surface?

2. you need to separate the vertical component from the horizontal

you use the vertical to find out the time he was in the air

its easier to calculate the time he took to drop from the highest point (0.8) till he got to the ground and then multiply by 2
$0=0.8-\frac{1}{2} g t^{2}$
t=0.4s
total time 0.8s

the vertical speed is simply
$0.8=0.4v_y-\frac{1}{2} g 0.4^{2}$
$v_y=4m/s$
you can also use energy conservation to find it

next you use the horizontal data to find out the horizontal speed
$v_x=\frac{d}{t}$
$v_x=\frac{8.04}{0.8}=10.05m/s$

so $v=10.05 \vec{e_x}+4 \vec{e_y} (m/s)$

its similar for the moon, only changes g value