For a scene in a movie, a stunt driver drives a 1.90 103 kg pickup truck with a length of 4.09 m around a circular curve with a radius of curvature of 0.333 km (Fig. 7.29). The truck is to curve off the road, jump across a gully 10.0 m wide, and land on the other side 2.96 m below the initial side. What is the minimum centripetal acceleration the truck must have in going around the circular curve to clear the gully and land on the other side?

Question

For a scene in a movie, a stunt driver drives a 1.90 103 kg pickup truck with a length of 4.09 m around a circular curve with a radius of curvature of 0.333 km (Fig. 7.29). The truck is to curve off the road, jump across a gully 10.0 m wide, and land on the other side 2.96 m below the initial side. What is the minimum centripetal acceleration the truck must have in going around the circular curve to clear the gully and land on the other side?

Answer 1

To calculate the minimum centripetal acceleration the truck must have in order to clear the gully and land on the other side, we'll apply the principles of circular motion and use the following steps:

Step 1: Calculate the maximum velocity of the truck
To clear the gully, the truck should achieve enough horizontal velocity. We can calculate the maximum velocity using the conservation of energy principle. The initial potential energy is converted into the final kinetic energy:

Initial potential energy = Final kinetic energy

mgh = (1/2)mv^2

Here, m represents the mass of the truck (1.90 x 10^3 kg), g represents the acceleration due to gravity (9.8 m/s^2), h represents the height difference (2.96 m), and v represents the maximum velocity of the truck.

Solving this equation for v, we get:

v = sqrt(2gh)

Substituting the given values, we have:

v = sqrt(2 * 9.8 m/s^2 * 2.96 m)

v ≈ 7.83 m/s

Step 2: Calculate the minimum centripetal acceleration
The minimum centripetal acceleration can be calculated using the relationship between velocity (v), radius of curvature (r), and acceleration (a):

a = v^2 / r

Substitute the given values, we have:

a = (7.83 m/s)^2 / (0.333 km) = (7.83 m/s)^2 / (0.333 x 1000 m)

a ≈ 185.56 m/s^2

So, the minimum centripetal acceleration the truck must have to clear the gully and land on the other side is approximately 185.56 m/s^2.

Answer 2

Calculate the minimum V necessary to jump across the gully. Do this by using the maximum distance it can fall while crossing the gully. That gives you a minumum allowed time to fall.

Gully width)/(max fall time)
= minumum speed

Once you have V, the centripetal acceleration is V^2/R(