A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 24 degrees below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of 4.8m/s/s and travels 54m to the edge of the cliff. The cliff is 32m above the ocean. The acceleration of gravity is 9.81m/s/s/

How long is the car in the air?
What is the car's position relative to the base of the cliff when the car lands in the ocean?

find the velocity at the end of the roll. Break that velocity into horizontal, and vertical components.

Now let the car fall 32m it that initial vertical velocity, using
d=vo*t +1/2 g t^2 and solve for time.

To find out how long the car is in the air, we need to calculate its time of flight. We can do this by using the kinematic equation for vertical motion:

y = y0 + v0y * t - (1/2) * g * t^2

Where:
y = vertical displacement (relative to the base of the cliff) = -32m (negative because it is below the base of the cliff)
y0 = initial vertical position = 0
v0y = initial vertical velocity = 0 (the car is initially at rest)
g = acceleration due to gravity = 9.81m/s^2 (downward direction)
t = time of flight (what we need to find)

Plugging in the values, we have:

-32 = 0 + 0 * t - (1/2) * 9.81 * t^2

Simplifying the equation:

-16.05t^2 = -32

Dividing both sides by -16.05:

t^2 = 1.99

Taking the square root of both sides (ignoring the negative root since time cannot be negative in this case):

t ≈ 1.41 seconds

Therefore, the car is in the air for approximately 1.41 seconds.

Now, let's determine the car's position relative to the base of the cliff when it lands in the ocean. We can use the equation of motion to calculate the horizontal displacement:

x = x0 + v0x * t + (1/2) * a * t^2

Where:
x = horizontal displacement (relative to the base of the cliff)
x0 = initial horizontal position = 0
v0x = initial horizontal velocity = 0 (the car is initially at rest horizontally)
a = acceleration = 0 (since there is no horizontal force acting on the car once it starts rolling)
t = time of flight = 1.41 seconds (from the previous calculation)

Plug in the values:

x = 0 + 0 * 1.41 + (1/2) * 0 * (1.41)^2

Simplifying the equation:

x = 0

This means that the car's horizontal displacement relative to the base of the cliff is 0. So, when the car lands in the ocean, it is directly below the base of the cliff.