A stone is thrown horizontally from a height of 45 m. How long will it take to h

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Question: A stone is thrown horizontally from a height of 45 m. How long will it take to hit the ground? (Take g = 10 m/s²) (2023)

Options:

Correct Answer: 3 s

Solution:

Using h = 0.5 * g * t^2, we have 45 = 0.5 * 10 * t^2. Solving gives t^2 = 9, so t = 3 s.

A stone is thrown horizontally from a height of 45 m. How long will it take to hit the ground? (Take g = 10 m/s²) (2023)

A stone is thrown horizontally from a height of 45 m. How long will it take to hit the ground? (Take g = 10 m/s²) (2023)

Step 1: Identify the height from which the stone is thrown. In this case, the height (h) is 45 meters.
Step 2: Recall the formula for the distance fallen under gravity: h = 0.5 * g * t^2, where g is the acceleration due to gravity (10 m/s²) and t is the time in seconds.
Step 3: Substitute the known values into the formula: 45 = 0.5 * 10 * t^2.
Step 4: Simplify the equation: 45 = 5 * t^2 (since 0.5 * 10 = 5).
Step 5: To isolate t^2, divide both sides by 5: t^2 = 45 / 5, which simplifies to t^2 = 9.
Step 6: Take the square root of both sides to find t: t = √9, which gives t = 3 seconds.

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 determine the time of fall based on height and acceleration due to gravity.