Yuvi is trying out for the track & field team and wants to give long jump a try. He currently can reach a distance of 5.90 m when leaving the ground at an angle of 30.0°.
(a) What is his takeoff speed?
(b) If Yuvi could increase his takeoff speed 5.0%, how much further would he be able to the jump?
let speed = s
u = s cos 30
Vi = s sin 30 = s/2
v = s/2 - g t = s/2 - 9.81 t
so
0 = s/2 - 9.81 t at the top where v = 0
so
t = s/(2*9.81)
2 t = time in air = s/9.81
range = u * time in air
5.90 = s cos 30 * s/9.81
s^2 = 9.81 *5.90 /cos 30
so
s = 66.8 meters/second
now do it for
s = 1.05 * 66.8