How to Calculate the Height of a Cliff and the Velocity of a Falling Stone
What is the height of the cliff and the velocity with which the stone reaches the ground?
Given that a stone dropped from the top of a cliff reaches its foot in 4 seconds, calculate the height of the cliff and the velocity at which the stone hits the ground (g=9m/s).
Answer:
The height of the cliff is 72 meters, and the stone reaches the ground with a velocity of 36 m/s.
Final answer: Using the principles of physics and the given time and gravity constant, we can determine that the height of the cliff is 72 meters, and the stone hits the ground with a velocity of 36 m/s.
Explanation: According to the principles of physics, we can determine the height of the cliff and the velocity of the stone as it hits the ground. Given a time of 4 seconds and a gravity constant (g) of 9 m/s², the height of the cliff can be calculated using the equation h = 0.5*g*t², where h stands for height and t is the time during which the object is falling. Substituting the provided values, we get h = 0.5 * 9 * 4² = 72 meters.
Similarly, the final velocity of the stone when it reaches the ground can be calculated using the equation v = g*t. Substituting the provided values, we get v = 9 * 4 = 36 m/s. Thus, the stone hits the ground with a velocity of 36 m/s.
Note that these calculations assume no air resistance.