What is the maximum height that the pole-vaulter can reach?

Question

A pole-vaulter of mass 75 kg reaches a maximum speed of 7 m/s just before he jams his pole into the notch to launch himself over the bar. Assuming that his pole is only 80% efficient, what is the maximum height that the pole-vaulter can reach?

Answer 1

The pole-vaulter converts his kinetic energy (KE) when he was running to gravitational potential energy (PE_G). (As he's going higher, he gains gravitational potential energy.) Since the pole is only 80% efficient, only 80% of the kinetic energy gets converted to gravitational potential energy. So, PE_G = 0.8*KE.

PE_G = 0.8*KE.

M*g*h = 0.8 *(0.5*M*v^2) M, h, and v are the vaulter's mass, height, and speed, respectively.

g*h = 0.8*0.5*v^2 Divide both sides by M (the mass).

g*h = 0.4*v^2

(9.81 m/s^2)*h = 0.4*(7 m/s)^2. Note that m and s denote meter and second, respectively.

h = 0.4*(7 m/s)^2 /(9.81 m/s^2) Divide both sides by 9.81 m/s^2. Also, note that m is NOT mass here.

= 0.4*(49 m^2/s^2)/(9.81 m/s^2)

= 0.4*49 m/9.81

= 1.99796 meters

I hoped this helped you and wish you a great school year. If you have any questions about this solution, feel free to leave a comment. :)