A rock is dropped from a tree of height 36.5 m into a lake (depth 9 m) below. After entering the water, the rock then floats gently down through the water at a speed of 12.5 m/s to the bottom of the lake. What is the total elapsed time?
To find the total elapsed time, we need to calculate the time it takes for the rock to fall from the tree to the bottom of the lake, as well as the time it takes for the rock to float down through the water.
First, let's find the time it takes for the rock to fall from the tree to the water surface.
Using the equation of motion:
h = (1/2) * g * t^2
Where h is the height (36.5 m), g is the acceleration due to gravity (9.8 m/s^2), and t is the time.
Rearranging the equation to solve for t:
t = sqrt(2h/g)
t = sqrt(2 * 36.5 / 9.8)
t ≈ 2.855 seconds
So, it takes approximately 2.855 seconds for the rock to fall from the tree to the water surface.
Next, let's find the time it takes for the rock to float down through the water.
We know that the speed of the rock while floating down through the water is 12.5 m/s. The depth of the lake is 9 m. Hence, the time it takes for the rock to reach the bottom of the lake can be calculated using the equation:
t = d / v
Where d is the depth of the lake (9 m) and v is the speed of the rock (12.5 m/s).
t = 9 / 12.5
t = 0.72 seconds
So, it takes approximately 0.72 seconds for the rock to reach the bottom of the lake.
Finally, we can find the total elapsed time by adding the time it takes for the rock to fall from the tree to the water surface and the time it takes for the rock to float down through the water.
Total elapsed time = Time to fall + Time to float
Total elapsed time = 2.855 + 0.72
Total elapsed time ≈ 3.575 seconds
Therefore, the total elapsed time is approximately 3.575 seconds.