A stone is thrown horizontally from the top of a cliff 45 m high. How long does

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Question: A stone is thrown horizontally from the top of a cliff 45 m high. How long does it take to hit the ground? (g = 10 m/s²)

Options:

Correct Answer: 4 s

Solution:

Using h = 0.5 * g * t^2, rearranging gives t = sqrt(2h/g) = sqrt(2 * 45 / 10) = sqrt(9) = 3 s.

A stone is thrown horizontally from the top of a cliff 45 m high. How long does it take to hit the ground? (g = 10 m/s²)

A stone is thrown horizontally from the top of a cliff 45 m high. How long does it take to hit the ground? (g = 10 m/s²)

Step 1: Identify the height of the cliff, which is 45 meters.
Step 2: Identify the acceleration due to gravity, which is given as g = 10 m/s².
Step 3: Use the formula for the height fallen under gravity: h = 0.5 * g * t².
Step 4: Rearrange the formula to solve for time (t): t = sqrt(2h/g).
Step 5: Substitute the values into the rearranged formula: t = sqrt(2 * 45 / 10).
Step 6: Calculate the value inside the square root: 2 * 45 = 90, and 90 / 10 = 9.
Step 7: Take the square root of 9: sqrt(9) = 3.
Step 8: Conclude that it takes 3 seconds for the stone to hit the ground.

Projectile Motion – The question tests understanding of the motion of an object under the influence of gravity, specifically how vertical motion is independent of horizontal motion.
Kinematic Equations – The use of the kinematic equation h = 0.5 * g * t^2 to calculate the time of free fall from a height.