A 1.0 kg rock is dropped from a height of 6.0 m. At what height is the rock\'s k

Question

A 1.0 kg rock is dropped from a height of 6.0 m. At what height is the rock's kinetic energy three times that of it potential energy (in m)? Take the potential energy to be 0 when the rock hits the ground. Two ice skaters stand together and push off of each other so that they travel in opposite directions on the ~frictionless ice. The larger ice skater has a velocity of -0.50 m/s (that is. 0.50 m/s to the left) and weighs 735 N. The smaller ice skater weighs 490 N. What will be her velocity in m/s after pushing off. Answer should be negative if to the left and positive if to the right (but you don't need to include the + sign if your answer is positive, only the - sign if negative).

Explanation / Answer

Here ,

let the height , as when the kinetic energy of rock is three times that of potential energy

potential energy of rock = 1/4 * initial kinetic energy of rock

m * g * h = m * g h0/4

h= 6/4

h = 1.5 m

the height of rock is 1.5 m

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let her velocity is vf

Now , Using conservation of momentum

735 * (- 0.50) + 490 * Vf = 0

Vf = 0.75 m/s

the velocity of smaller skater is 0.75 m/s

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