An object is thrown horizontally from the top of a cliff 80 m high. How long does it take to hit the ground?
Practice Questions
1 question
Q1
An object is thrown horizontally from the top of a cliff 80 m high. How long does it take to hit the ground?
2 s
4 s
5 s
8 s
Using h = (1/2)gt^2, we have 80 = (1/2)(9.8)t^2, solving gives t ≈ 4 s.
Questions & Step-by-step Solutions
1 item
Q
Q: An object is thrown horizontally from the top of a cliff 80 m high. 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: 10
Step 1: Identify the height of the cliff, which is 80 meters.
Step 2: Understand that the object is thrown horizontally, so we only need to consider the vertical motion to find out how long it takes to hit the ground.
Step 3: Use the formula for the distance fallen under gravity: h = (1/2)gt^2, where h is the height (80 m), g is the acceleration due to gravity (approximately 9.8 m/s²), and t is the time in seconds.
Step 4: Substitute the values into the formula: 80 = (1/2)(9.8)t^2.
Step 5: Simplify the equation: 80 = 4.9t^2.
Step 6: To isolate t^2, divide both sides by 4.9: t^2 = 80 / 4.9.
Step 7: Calculate the right side: t^2 ≈ 16.33.
Step 8: Take the square root of both sides to find t: t ≈ √16.33.
Step 9: Calculate the square root: t ≈ 4.03 seconds.
Step 10: Round the answer to a reasonable number of significant figures: t ≈ 4 seconds.
