A car accidently rolls off a cliff.As it leaves the cliff it has a horizontal velocity of 13m/s, it hits the ground 60m from the shoreline.calculate the height of the cliff.
u = 13 m/s forever so
d = u t
60 meters = 13 m/s * t
t = 60/13 = 4.62 seconds in the air falling
h = (1/2) g t^2
h = (1/2) (9.81) (4.62)^2 = 104 meters
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To calculate the height of the cliff, we can use the equations of motion along with the information provided.
First, let's break down the given information:
Initial horizontal velocity of the car, u = 13 m/s
Distance traveled horizontally, x = 60 m
Now, we can use the equation for horizontal motion to find the time it takes for the car to travel 60 meters horizontally:
x = ut + (1/2)at^2
Since there is no horizontal acceleration, the equation becomes:
x = ut
Rearranging the equation to solve for time:
t = x / u
Plugging in the values:
t = 60 m / 13 m/s
t = 4.615 seconds
Now, we can use the equation for vertical motion to find the height of the cliff:
h = ut + (1/2)gt^2
Where h is the height, u is the initial vertical velocity, g is the acceleration due to gravity, and t is the time.
In this case, the initial vertical velocity is 0 m/s (since the car rolls off the cliff), and the acceleration due to gravity is approximately 9.8 m/s^2.
Plugging in the values:
h = (0 m/s) * (4.615 s) + (1/2)(9.8 m/s^2)(4.615 s)^2
h = (1/2)(9.8 m/s^2)(21.403 s^2)
h = 9.8 m/s^2 * 21.403 s^2 / 2
h = 105.167 m
Therefore, the height of the cliff is approximately 105.167 meters.