Physics question

Question

A child at a summer camp runs towards a 5 in rope at a speed of 4 m/s, grabbing on to the bottom of the rope. What will be the change in elevation for the child's center of gravity as she and the rope swing forward?

a) 0.82 m

b) 4.1 m

c) 0.21 m

Answer 1

Did you mean a 5 meter rope? ((BUT---does it matter?))

Solve this in terms of energy. While running, the child has kinetic energy, KE = 1/2 * m * v2 . v = 4m/sec, so the energy is 8*m

When the rope pulls her up, the KE is converted to potential energy. PE. When she stops moving, PE = m*g*h, where g is the acceleration of gravity, and h is the height.

So PE = m*9.8*h

Putting it together: PE = KE

m * 9.8 * h = 8 * m

h = 8 / 9.8