A stone is dropped into a deep well and is heard to hit the water 2.95 s after being dropped. Determine the depth of the well.
Solve this equation for the depth, H:
T = 2.95s = (time to fall) + (time for sound to arrive)
= sqrt(2H/g) + H/(340 m/s)
Convert it to a quadratic equation for H and solve for the positive root.
Water flows (velocity initial=0) over a dam at the rate of 660 kg/s and falls vertically 81 m before striking the turbine blades. Calculate the rate at which mechanical energy is transfered to the turbine blades, assuming 55% efficiency.
s=ut 1/2 at�0…5
s=o(2.95) 1/2(9.8)(2.95)�0…5
s=0 42.64
s=42.64 m (approx.)
To determine the depth of the well, we can use the equations of motion and apply the principles of kinematics.
Let's consider the following variables:
- h: the depth of the well (the distance the stone falls)
- g: acceleration due to gravity (approximately 9.8 m/s²)
- t: the time taken for the stone to hit the water (2.95 seconds)
We can use the equation for the vertical displacement:
h = 0.5 * g * t^2
Now, we can substitute the given values into the equation:
h = 0.5 * 9.8 m/s² * (2.95 s)^2
Simplifying the equation:
h = 0.5 * 9.8 m/s² * 8.7025 s²
h = 42.71525 m
Therefore, the depth of the well is approximately 42.7 meters.