A car traveling at 40 m/s runs out of gas while traveling up a 7.0 ∘ slope

How far will it coast before starting to roll back down?

To find the distance the car will coast before starting to roll back down, we need to use the concept of potential energy and kinetic energy.

Step 1: Determine the initial potential energy of the car at the top of the slope.

The potential energy (PE) can be calculated using the formula:

PE = mgh

Where:
m = mass of the car
g = acceleration due to gravity
h = height

However, in this case, we are given the slope angle (θ) instead of the height. We can calculate the height using the slope angle and the distance along the slope (d) using the formula:

h = dsin(θ)

Step 2: Determine the height of the slope.

In this case, we are given the slope angle (θ = 7.0 ∘) and the distance along the slope (d). We can calculate the value of h using the formula mentioned above.

Step 3: Determine the potential energy.

Using the calculated height (h) and the given mass of the car, we can calculate the potential energy (PE).

Step 4: Determine the kinetic energy.

Since the car has run out of gas and is not being propelled anymore, the kinetic energy becomes zero.

Step 5: Equate potential energy to kinetic energy.

At the top of the slope, the potential energy is equal to the kinetic energy at the point where the car starts to roll back down.

PE = KE

Step 6: Solve for the distance coasted.

Using the equation from Step 5 and the calculated values for potential energy (PE) and kinetic energy (KE), we can solve for the distance (d) the car will coast before starting to roll back down.

d = h / tan(θ)

Now let's substitute the values into the equations and calculate the distance:

Given:
Velocity (v) = 40 m/s
Slope angle (θ) = 7.0 ∘

Step 1: Determine the height of the slope
h = d * sin(θ)

Step 2: Calculate the height
h = d * sin(7.0 ∘)

Step 3: Calculate the potential energy
PE = m * g * h

Step 4: The car has run out of gas, so the kinetic energy is zero.

Step 5: Equate potential energy to kinetic energy.

PE = KE

Step 6: Solve for the distance coasted
d = h / tan(θ)

By following these steps and substituting the given values into the equations, you can find the distance the car will coast before starting to roll back down the slope.

52m