Question

A 50 kg granite boulder gets dislodged from a cliff of height 20 m and undergoes an absolute vertical free fall. If the acceleration due to gravity is 10 m/s\(^2\), the boulder will hit the ground with a velocity of _________ m/s.

Hint:

The final velocity of an object in free fall can be calculated using the kinematic equation, which relates the height of the fall, acceleration due to gravity, and the initial velocity (which is zero if the object is dropped).

Answer 1

Correct Answer: 20

Step 1: Use the Kinematic Equation for Free Fall.
When an object falls freely under gravity, its final velocity \(v\) can be calculated using the following kinematic equation: \[ v^2 = u^2 + 2gh, \] where \(v\) is the final velocity, \(u\) is the initial velocity (which is 0 m/s for a free fall from rest), \(g\) is the acceleration due to gravity, and \(h\) is the height from which the object falls. Substituting the given values: \[ v^2 = 0^2 + 2 \times 10 \times 20, \] \[ v^2 = 400, \] \[ v = \sqrt{400} = 20 \, \text{m/s}. \] Step 2: Conclusion.
The boulder will hit the ground with a velocity of 20 m/s.