A car acchdently 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. What is the height of the cliff?
8m
2060
150
To find the height of the cliff, we can use the equations of motion and apply the principles of projectile motion.
Let's break down the problem into its components:
1. Vertical motion: The car falls vertically downward due to the force of gravity.
2. Horizontal motion: The car moves horizontally with a constant velocity.
We need to use the equation that relates the vertical displacement to the initial vertical velocity, time, and acceleration due to gravity:
h = (1/2) * g * t^2
Where:
h is the height of the cliff,
g is the acceleration due to gravity (approximately 9.8 m/s^2),
t is the time taken by the car to hit the ground.
First, let's find the time taken by the car to hit the ground:
Using the horizontal velocity and the distance from the shoreline, we can calculate the time taken using the formula:
d = v * t
Where:
d is the horizontal distance (60m)
v is the horizontal velocity (13 m/s)
t is the time taken to hit the ground (which we need to find)
Rearranging the equation, we have:
t = d / v = 60m / 13 m/s
Now, we can calculate the time taken by the car to hit the ground using the given values:
t = 4.615 seconds (approx.)
Now that we have the time, we can substitute it into the equation for vertical motion to find the height of the cliff:
h = (1/2) * g * t^2
h = (1/2) * 9.8 m/s^2 * (4.615s)^2
h ≈ 107.8 meters
Therefore, the height of the cliff is approximately 107.8 meters.