A stone is thrown horizontally from the top of a cliff 45 m high. How long does it take to hit the ground? (Assume g = 10 m/s²)
Practice Questions
1 question
Q1
A stone is thrown horizontally from the top of a cliff 45 m high. How long does it take to hit the ground? (Assume g = 10 m/s²)
3 s
4 s
5 s
6 s
Using h = 0.5 * g * t^2, rearranging gives t = sqrt(2h/g) = sqrt(2 * 45 / 10) = sqrt(9) = 3 s.
Questions & Step-by-step Solutions
1 item
Q
Q: A stone is thrown horizontally from the top of a cliff 45 m high. How long does it take to hit the ground? (Assume g = 10 m/s²)
Solution: Using h = 0.5 * g * t^2, rearranging gives t = sqrt(2h/g) = sqrt(2 * 45 / 10) = sqrt(9) = 3 s.
Steps: 8
Step 1: Identify the height of the cliff, which is 45 meters.
Step 2: Recognize that the stone 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 = 0.5 * g * t^2, where h is the height (45 m), g is the acceleration due to gravity (10 m/s²), and t is the time in seconds.
Step 4: Rearrange the formula to solve for 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 then 90 / 10 = 9.
Step 7: Take the square root of 9, which is 3.
Step 8: Conclude that it takes 3 seconds for the stone to hit the ground.
