A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 22◦ 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 4.3 m/s2 and travels 43 m to the edge of the cliff. The cliff is 33 m above the ocean.

How long is the car in the air? The acceler- ation of gravity is 9.81 m/s2 .
Answer in units of s
What is the car’s position relative to the base of the cliff when the car lands in the ocean?
Answer in units of m

V^2 = Vo^2 + 2a*d

V^2 = 0 + 8.6*43 = 369.8
V = 19.23 m/s At the edge of ihe cliff.

Vo = 19.23m/s[-22o] At the edge of the cliff.
Xo = 19.23*cos(-22) = 17.83 m/s.
Yo = 19.23*sin(-22)=-7.20 m/s.=7.20 m/s,
downward.

a. h = Yo*t + 0.5g*t^2 = 33 m.
4.9t^2 + 7.2t - 33 = 0
Use Quadratic Formula.
t = 1.96 s. In air.

b. Dx=Xo * t = 17.83m/s * 1.96s=34.9 m

To find the time the car is in the air, we can use the kinematic equation:

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

Where:
s = distance (43 m)
u = initial velocity (0 m/s)
a = acceleration (-9.81 m/s^2, since the car is moving downwards and gravity is acting against it)
t = time in the air (what we're trying to find)

Rearranging the equation to solve for t, we have:

t = √(2s/a)

Plugging in the values, we get:

t = √(2 * 43 m / -9.81 m/s^2)

Calculating this, we find:

t ≈ 3.30 s

Therefore, the car is in the air for approximately 3.30 seconds.

To find the car's position relative to the base of the cliff when it lands in the ocean, we need to calculate the horizontal distance the car travels during this time. Since the acceleration is acting vertically, it does not affect the horizontal motion.

The horizontal distance can be found using the equation:

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

Where:
d = horizontal distance
u = initial velocity (0 m/s)
a = acceleration (0 m/s^2, since there is no horizontal acceleration)
t = time in the air (3.30 s)

Plugging in the values, we get:

d = 0 m/s * 3.30 s + (1/2) * 0 m/s^2 * (3.30 s)^2

Simplifying this, we find:

d = 0 m

Therefore, the car's position relative to the base of the cliff when it lands in the ocean is 0 meters, indicating that it lands directly below the edge of the cliff.