For a scene in a movie, a stunt driver drives a 1.50×103kg SUV with a length of 4.30m around a circular curve with a radius of curvature of 0.333 km (Figure 1) . The vehicle is to be driven off the edge of a gully 10.0 m wide, and land on the other side 2.96 m below the initial side.


Part A
What is the minimum centripetal acceleration the SUV must have in going around the circular curve to clear the gully and land on the other side?

To find the minimum centripetal acceleration the SUV must have to clear the gully and land on the other side, we can use the principle of conservation of mechanical energy.

First, let's find the speed of the SUV as it clears the gully. We can use the conservation of mechanical energy equation:

ME_initial = ME_final

The initial mechanical energy consists of the kinetic energy and the potential energy:

ME_initial = KE_initial + PE_initial

The final mechanical energy consists of the kinetic energy and the potential energy:

ME_final = KE_final + PE_final

Since the SUV is driving on a flat surface, the potential energy at the starting side and the landing side is the same, so we can neglect it for this calculation.

Therefore, we can rewrite the conservation of mechanical energy equation as:

KE_initial = KE_final

The kinetic energy is given by the equation:

KE = (1/2) * m * v^2

where m is the mass of the SUV and v is its velocity.

Rearranging the equation to solve for v, we get:

v = sqrt((2 * KE) / m)

Now we need to find the kinetic energy of the SUV at the starting side and the landing side.

At the starting side, the SUV only has potential energy. The potential energy is given by the equation:

PE = m * g * h

where m is the mass of the SUV, g is the acceleration due to gravity, and h is the height from the starting side to the landing side.

Since we're given that the height is 2.96 m, we can calculate the potential energy at the starting side.

Now, the minimum centripetal acceleration the SUV must have to clear the gully and land on the other side is the acceleration required to keep the car moving in a circular path. This acceleration is given by the equation:

a = v^2 / r

where v is the velocity and r is the radius of curvature of the circular path.

Now we can substitute the values we have calculated into this equation to find the minimum centripetal acceleration.