A stone is dropped from the peak of a hill. It covers a distance of 45 meters in ther last two seconds of its motion. Find the height of the peak?

Question

A stone is dropped from the peak of a hill. It covers a distance of 45 meters in ther last two seconds of its motion. Find the height of the peak?

Answer 1

To find the height of the peak, we need to use the formula for the displacement of an object in free fall:

𝑑 = (1/2)𝑔𝑡²

Where:
𝑑 is the displacement (distance),
𝑔 is the acceleration due to gravity (approximately 9.8 m/s²),
and 𝑡 is the time.

In this case, we know that the stone covers a distance of 45 meters in the last two seconds of its motion. So, we can set up the equation as follows:

45 = (1/2) * 9.8 * (2)²

Simplifying the equation:

45 = 4.9 * 4

Now, let's solve for the displacement (distance) covered by the stone during its entire motion:

𝑑 = (1/2) * 9.8 * 𝑡²

𝑑 = 4.9 * 𝑡²

Since the stone covers a distance of 45 meters in the last two seconds of its motion, we need to find the total time it takes to cover this distance. We can solve for time by rearranging the equation:

𝑡² = 45 / 4.9

𝑡² ≈ 9.1837

Now, we can solve for time (𝑡) by taking the square root of both sides:

𝑡 ≈ √9.1837

𝑡 ≈ 3.03 seconds (rounded to two decimal places)

Finally, substitute this value back into the equation to find the height (𝑑):

𝑑 = (1/2) * 9.8 * (3.03)²

𝑑 ≈ 44.98 meters (rounded to two decimal places)

Therefore, the height of the peak of the hill is approximately 44.98 meters.