An object is thrown horizontally from the top of a cliff of height 80 m. How long does it take to hit the ground?

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Q: An object is thrown horizontally from the top of a cliff of height 80 m. How long does it take to hit the ground?

Solution: Using h = (1/2)gt^2, we have 80 = (1/2)(9.8)t^2, solving gives t ≈ 4 s.

Steps: 9

Step 1: Identify the height of the cliff, which is 80 meters.
Step 2: Use the formula for the distance fallen under gravity: h = (1/2)gt^2, where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time in seconds.
Step 3: Substitute the known values into the formula: 80 = (1/2)(9.8)t^2.
Step 4: Simplify the equation: 80 = 4.9t^2 (since (1/2) * 9.8 = 4.9).
Step 5: To isolate t^2, divide both sides by 4.9: t^2 = 80 / 4.9.
Step 6: Calculate the right side: t^2 ≈ 16.33.
Step 7: Take the square root of both sides to find t: t ≈ √16.33.
Step 8: Calculate the square root: t ≈ 4.04 seconds.
Step 9: Round the answer to the nearest whole number: t ≈ 4 seconds.