An object is dropped from a cliff and reaches a velocity of 47.5 m/s at the time of impact. a) How high is the cliff? b)How long did it take to hit the river below?
To find the answers to these questions, we can use the equations of motion for freely falling objects. Let's break down the problem step by step.
a) To determine the height of the cliff, we need to find the initial velocity and the time it took for the object to reach the velocity of 47.5 m/s at the time of impact. We'll assume that the object was dropped, meaning its initial velocity is 0 m/s.
The equation we can use is:
v^2 = u^2 + 2as
where:
v = final velocity (47.5 m/s)
u = initial velocity (0 m/s)
a = acceleration due to gravity (-9.8 m/s^2, considering it's directed downwards)
s = distance traveled (height of the cliff)
Rearranging the equation, we get:
s = (v^2 - u^2) / (2a)
Substituting the given values, we have:
s = (47.5^2 - 0) / (2 * -9.8)
Simplifying this equation, we find:
s = 1130.625 / -19.6
s ≈ -57.9 meters
We consider the negative value because the height is measured in the opposite direction to the acceleration due to gravity. Therefore, the height of the cliff is approximately 57.9 meters.
b) To calculate the time it took for the object to hit the river below, we can use a different equation of motion:
v = u + at
where:
v = final velocity (47.5 m/s)
u = initial velocity (0 m/s)
a = acceleration due to gravity (-9.8 m/s^2)
t = time taken
Simplifying this equation, we have:
47.5 = 0 + (-9.8)t
47.5 = -9.8t
t ≈ 4.85 seconds
Therefore, it took approximately 4.85 seconds for the object to hit the river below.