In a stunt for a movie, a remote controlled car is driven horizontally of the edge of a cliff at a speed of 35m/s. The car hits the ground 85m from the base of the cliff. How high is the cliff?

The car is in the air for a time

t = 85/35 = 2.429 seconds

The cliff height is how far the car falls during that time. Calculate it with:

h = (g/2)*t^2

To determine the height of the cliff, we can use the equations of motion. We will use the equation that relates time, initial velocity, and acceleration to find the time it takes for the car to hit the ground. Then, we can use this time to calculate the height of the cliff using the equation that relates height, time, and the initial vertical velocity.

Step 1: Find the time it takes for the car to hit the ground.
We know that the initial vertical velocity (u) is zero because the car is driven horizontally off the edge of the cliff. The acceleration due to gravity (g) is approximately 9.8 m/s^2.

We can use the equation:
s = ut + (1/2)gt^2

where:
s = displacement (85m, distance from the base of the cliff)
u = initial vertical velocity (0 m/s)
g = acceleration due to gravity (-9.8 m/s^2)
t = time

Plugging in the values, the equation becomes:
85 = 0*t + (1/2)(-9.8)*t^2

Simplifying the equation, we get:
85 = (-4.9)*t^2

Rearranging the equation, we get a quadratic equation:
4.9t^2 - 85 = 0

Step 2: Solve the quadratic equation.
To solve the quadratic equation, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 4.9, b = 0, and c = -85. Plugging in these values, the quadratic formula becomes:
t = (√(0^2 - 4(4.9)(-85))) / (2(4.9))

Simplifying further, we get:
t = (√(0 + 1666)) / 9.8
t = (√1666) / 9.8

Using a calculator, we find that t ≈ 5.13 seconds (rounded to two decimal places).

Step 3: Calculate the height of the cliff.
To find the height of the cliff, we can use the equation:
h = ut + (1/2)gt^2

where:
h = height of the cliff
u = initial vertical velocity (0 m/s)
g = acceleration due to gravity (-9.8 m/s^2)
t = time (5.13 seconds, rounded to two decimal places)

Plugging in the values, the equation becomes:
h = 0*5.13 + (1/2)(-9.8)*(5.13)^2

Simplifying the equation, we get:
h = (-4.9)*(5.13)^2

Using a calculator, we find that h ≈ 129.22 meters (rounded to two decimal places).

Therefore, the height of the cliff is approximately 129.22 meters.