Seen similar problems solved but when I solve this one the same way and put into cengage it tells me my answer is wrong. Not sure what I'm doing incorrectly.

Question

A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 19.0° 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 3.06 m/s² for a distance of 45.0 m to the edge of the cliff, which is 50.0 m above the ocean.

(a) Find the car's position relative to the base of the cliff when the car lands in the ocean

(b) Find the length of time the car is in the air

Answer 1

Here is a sketch:

The v_i that is shown is the initial velocity of the car flying off the cliff but it is also the final velocity of the car accelerating down the ramp.

The final velocity of the car accelerating down the cliff can be found using:

v_f² = v_i² + 2ax where v_f is the final velocity at the end of the ramp (which equals the velocity of the car as it leaves the cliff), v_i = 0 since the car starts at rest, a = 3.06, and x = 45 so:

v_f² = 0 + 2(3.06)(45) = 275.4

v_f = √275.4 = 16.595 m/s

which means the vi in our sketch (the velocity that the car leaves the edge of the cliff) is 16.595 m/s

BUT it leaves at an angle of 19°

To find v_i-x and v_i-y we must use trig:

v_i-x = v_icos(θ) = 16.595cos(19°) = 15.691 m/s

v_i-y = v_isin(θ) = 16.595sin(19°) = 5.403 m/s, going downward so v_i-y = -5.403 m/s

To find the time the car it in the air, use:

x = v_it + 1/2at² where x = -50 m, v_i = v_i-y = 5.403 m/s, and a = -9.81 m/s² so:

-50 = -5.403t + 1/2(-9.81)t²

4.905t² + 5.403t - 50 = 0

Using the Quadratic Formula, t = 2.689 seconds (we throw out the negative answer).

During that 2.689 seconds, the car travels in the x-direction at v_i-x = 15.691 m/s so d = (15.691)(2.689) = 42.19 meters

So the answer to "Find the car's position relative to the base of the cliff when the car lands in the ocean", is it is 42.2 meters from the base of the cliff

And the answer to "Find the length of time the car is in the air" is 2.69 seconds