When Will the Car Hit the Ocean?

[physicsquest]

Homework Statement

A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 24.0 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 4.00 m/s^2 for a distance of 50.0 m to the edge of the cliff which is 30.0m above the ocean. Find a.) the car's position relative to the base of the cliff when the car lands in the ocean and b.) the length of time the car is in the air.

Homework Equations

(vy)^2= (vo)^2 + (2ay)(yf-yo)

The Attempt at a Solution

 

[jbsteele]

a.) the car's final position relative to the base of the cliff will be 80.0 m below the base. b.) using the equation (vy)^2 = (vo)^2 + (2ay)(yf-yo), I solve for t, which is 5.00 s.

 

[tomcue]

a.) To find the car's position relative to the base of the cliff, we first need to find the horizontal distance the car travels before reaching the edge of the cliff. We can use the equation for horizontal distance, x = vo*t + (1/2)*a*t^2, where vo = 0 and a = 4.00 m/s^2. Solving for t, we get t = (50.0 m)/(4.00 m/s^2) = 12.5 s.
Next, we can use the equation for vertical position, y = yo + vo*t + (1/2)*a*t^2, where yo = 30.0 m, vo = 0, and a = -9.8 m/s^2 (since the car is accelerating downwards due to gravity). Plugging in our values, we get y = 30.0 m + (0)*(12.5 s) + (1/2)*(-9.8 m/s^2)*(12.5 s)^2 = 30.0 m - 76.56 m = -46.56 m. Therefore, the car's position relative to the base of the cliff when it lands in the ocean is -46.56 m.

b.) To find the length of time the car is in the air, we can use the equation for vertical velocity, vy = vo + a*t, where vo = 0 and a = -9.8 m/s^2. Plugging in our values, we get vy = 0 + (-9.8 m/s^2)*(12.5 s) = -122.5 m/s. Since the car is in the air, it has a positive vertical velocity, so we can use the equation for time of flight, t = (2*vy)/a. Plugging in our values, we get t = (2*(-122.5 m/s))/(-9.8 m/s^2) = 25.0 s. Therefore, the length of time the car is in the air is 25.0 s.