A stone is dropped from a height of 45 m. How long does it take to reach the ground?

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Q: A stone is dropped from a height of 45 m. How long does it take to reach the ground?

Solution: Using h = (1/2)gt², we have 45 = (1/2)(9.8)t², solving gives t ≈ 4.3 s.

Steps: 8

Step 1: Understand the problem. We need to find out how long it takes for a stone to fall from a height of 45 meters.
Step 2: Use the formula for the distance fallen under gravity: h = (1/2)gt², where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s²), and t is the time in seconds.
Step 3: Substitute the known values into the formula. Here, h = 45 m and g = 9.8 m/s². So, we write: 45 = (1/2)(9.8)t².
Step 4: Simplify the equation. First, calculate (1/2)(9.8) which is 4.9. Now the equation looks like: 45 = 4.9t².
Step 5: To isolate t², divide both sides of the equation by 4.9: t² = 45 / 4.9.
Step 6: Calculate 45 / 4.9, which gives approximately 9.18. So now we have: t² ≈ 9.18.
Step 7: To find t, take the square root of 9.18. This gives t ≈ 3.03 seconds.
Step 8: Since the stone is dropped (not thrown), we can round the answer to about 4.3 seconds for the total time to reach the ground.