Question

A 70 kg person can achieve the maximum speed of 2.5 m/s while running a 100 m dash. Treat the person as a point particle.

a. At this speed, what is the person's kinetic energy?
Express your answer with the appropriate units.
b. To what height above the ground would the person have to climb in a tree to increase his gravitational potential energy by an amount equal to the kinetic energy you calculated in part A?

Answer 1

a. 218.75 J b. 0.3125m

Step-by-step explanation:

A:

Kinetic energy is found using the formula
`KE = (1)/(2)*m*v^2`

Plugging in 2.5 m/s for velocity and 70 kg for mass we get 218.75 J

B:

To find the height the person has to reach for his kinetic energy to be equal to his potential energy you use the equation
`PE = m*g*h` and set the kinetic energy equation equal to the potential energy equations, in which you will get:

`(1)/(2)*m*v^2=m*g*h\\ (1)/(2)*v^2=g*h\\ h=(v^2)/(2g)`

h = 0.3125 meters