015 (part 1 of 2) 10.0 points

A car is parked on a cliff overlooking the
ocean on an incline that makes an angle of 21�
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 4.9 m/s2 and travels 41 m to the edge of
the cliff. The cliff is 24 m above the ocean.
How long is the car in the air? The acceler-
ation of gravity is 9.81 m/s2 .

To find out how long the car is in the air, we need to determine the time it takes for the car to reach the edge of the cliff.

We can start by calculating the time it takes for the car to travel the horizontal distance (41 m) to reach the edge of the cliff. Since the car is rolling down the incline with a constant acceleration, we can use the following equation of motion:

S = ut + (1/2)at^2

where:
S = displacement (41 m)
u = initial velocity (0 m/s, as the car starts from rest)
a = acceleration (4.9 m/s^2)
t = time

Rearranging the equation and substituting the given values, we have:

41 = (1/2)(4.9)(t^2)

Now, we can solve for t by isolating the variable:

82 = 4.9t^2

Divide both sides by 4.9:

t^2 = 16.73469

Take the square root of both sides to find t:

t = 4.095 s (rounded to three decimal places)

Therefore, it takes approximately 4.095 seconds for the car to reach the edge of the cliff horizontally.

Next, we need to calculate the time it takes for the car to fall from the cliff to the ocean. We can use the equation of motion to determine the time:

h = (1/2)gt^2

where:
h = height (24 m)
g = acceleration due to gravity (9.81 m/s^2)
t = time

Rearranging the equation and substituting the given values, we have:

24 = (1/2)(9.81)(t^2)

Simplifying:

48 = 9.81t^2

Divide both sides by 9.81:

t^2 = 4.892515

Take the square root of both sides:

t = 2.212 s (rounded to three decimal places)

Therefore, it takes approximately 2.212 seconds for the car to fall from the cliff to the ocean.

To find the total time the car is in the air, we add the time it takes for the car to travel horizontally and vertically:

Total time = 4.095 s + 2.212 s = 6.307 s (rounded to three decimal places)

Therefore, the car is in the air for approximately 6.307 seconds.