Step-by-step explanation:
To solve this problem, we need to calculate the time taken by the rock to fall from the tree to the surface of the water and the time taken by the rock to sink to the bottom of the lake.
Let's start by calculating the time taken by the rock to fall from the tree to the surface of the water. We can use the following kinematic equation:
h = 1/2 * g * t^2
where h is the height of the tree, g is the acceleration due to gravity (9.8 m/s^2), and t is the time taken by the rock to fall from the tree to the surface of the water.
Rearranging this equation to solve for t, we get:
t = sqrt(2h/g)
Substituting the given values, we get:
t = sqrt(2 * 26 / 9.8) = 2.03 seconds
So the time taken by the rock to fall from the tree to the surface of the water is 2.03 seconds.
Now, let's calculate the time taken by the rock to sink to the bottom of the lake. We can use the following formula:
t = d/v
where d is the depth of the lake (5.1 m) and v is the constant speed of the rock in water (1.6 m/s).
Substituting the given values, we get:
t = 5.1 / 1.6 = 3.19 seconds
So the time taken by the rock to sink to the bottom of the lake is 3.19 seconds.
The total elapsed time is the sum of the time taken by the rock to fall from the tree to the surface of the water and the time taken by the rock to sink to the bottom of the lake:
total elapsed time = 2.03 + 3.19 = 5.22 seconds
Therefore, the total elapsed time is 5.22 seconds.