A high jumper of mass 80kg reaches the end of his run up with 2100 of kinetic energy (k.e.). At take off he drives off the ground adding 800J to his kinetic energy . Stating any assumptions you make estimate
(a) the speed of the high jumper at the end of his run up
(b) the height of the bar which he could clear if his k.e. at the top of his jump is 1700J
Thanks for your help :)
(a) the speed of the high jumper at the end of his run up
(b) the height of the bar which he could clear if his k.e. at the top of his jump is 1700J
Thanks for your help :)
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If we assume that the high-jumper's take-off is a perfectly elastic "collision" with the ground (so no energy is lost as heat (ground friction & air resistance) or in the deformation of the ground etc) then all energy is conserved and the loss of k.e. will equal the gain in GPE (= mgh).
(a) k.e at end of run-up = 2100J = 0.5*m*v^2 = 0.5*80*v^2
so speed at end of run-up is
v = sqrt(2100/40) m/s = 7.25 m/s
(b) Total k.e. at take-off = 2100 + 800J = 2900J
k.e. lost = 2900 - 1700J = 1200J = GPE gained
m*g*h = 1200J
So height of bar is h = 1200 / (80*9.8) m = 1.53 m
(a) k.e at end of run-up = 2100J = 0.5*m*v^2 = 0.5*80*v^2
so speed at end of run-up is
v = sqrt(2100/40) m/s = 7.25 m/s
(b) Total k.e. at take-off = 2100 + 800J = 2900J
k.e. lost = 2900 - 1700J = 1200J = GPE gained
m*g*h = 1200J
So height of bar is h = 1200 / (80*9.8) m = 1.53 m