Anthony T. answered • 11/02/20
Patient Science Tutor
The PE energy of a boulder 210 m from the ground is given by the formula
PE = h x m x g where h is the height above the ground, m is the mass, g is the acceleration of gravity.
Substituting the given data in to the equation gives
PE = 210m x 75 kg x 9.8 m/s^2 = 154350 J (150000J to significant figures)
The velocity when the boulder is 50 m from the ground is the velocity obtained by free-fall at 160 m from the top of the cliff (210m - 50m).
This velocity is obtainable from the equation
V^2 = Vo^2 + 2 x g x S where S is the distance fallen (160m), Vo = 0, g is positive as it is in the same direction as the final velocity. Substituting into the equation gives
V^2 = 2 x 9.8m/s^2 x 160m = 3136 m^2/s^2 taking the square root of V
V = 56 m/s as the velocity when the boulder has fallen 160m and is 50m from the ground.
Another approach to the velocity in question is to calculate the potential energy the boulder would have 50 m from the ground, subtract this from the starting potential energy. Equate the result to the kinetic energy it would have after falling to 50m above the ground (1/2 x 75kg x V^2) and solve for V which gives you the same velocity.
