A Student drops a rock from a bridge to the water 14.7m below. with what speed does the rock strike the water? the acceleration of gravity is 9.8 m/s^2. andswer in units of m/s.
To find the speed at which the rock strikes the water, we can use the equations of motion.
First, we need to determine the time it takes for the rock to fall from the bridge to the water. We can do this using the formula:
h = (1/2) * g * t^2
Where:
h = height (14.7m in this case)
g = acceleration due to gravity (9.8 m/s^2)
t = time
Rearranging the formula to solve for time (t), we get:
t^2 = 2h / g
t = √(2h / g)
Plugging in the given values, we have:
t = √(2 * 14.7 / 9.8)
≈ √3
≈ 1.73 seconds
Now that we know the time taken, we can find the speed of the rock using the formula:
v = g * t
Where:
v = velocity (speed)
g = acceleration due to gravity (9.8 m/s^2)
t = time (1.73 seconds)
Plugging in the values, we have:
v = 9.8 * 1.73
≈ 16.954 m/s
Therefore, the speed at which the rock strikes the water is approximately 16.954 m/s.