If a person glides through the air at a height of 215 m with a velocity of 25.4 m/s, suddenly they dive to a height of 178 m. What is the new velocity?
The person is originally gliding at a height 215 m with a velocity 25.4 m/s. A sudden dive to a height 178 m is made. It is not possible to estimate the velocity of the person at this level unless a few assumptions are made. It has to be assumed that air resistance is negligible and the difference in potential energy of the person at the two levels is completely converted to kinetic energy. As there is a drop in the potential energy of the person, there is an increase in kinetic energy. Let V represent the velocity of the person at 178 m. Using the law of conservation of energy gives:
m*g*215 - m*g*198 = (1/2)*m*V^2 - (1/2)*m*25.4^2
=> 9.8*(215 - 198) = V^2/2 - 25.4^2/2
=> 333.2 = V^2 - 25.4^2
=> V^2 = 978.36
=> `V ~~ 31.27`
The velocity of the person at 178 m has an approximate magnitude of 31.27 m/s