Question

You are assigned to do some calculations for a movie stunt that involves a car on a straight road. The road has a hill that rises 8.0 m above the flat region. The top of the hill is a circular arc of radius 20 m. You need to determine whether a car traveling under certain conditions will lose contact with the road at the top of the hill. There is a stop sign 50 m from the beginning of the hill. You are to assume that a car of mass 1600 kg accelerates uniformly from rest at the stop sign, has a speed of 17 m/s when it reaches the beginning of the hill, and then coasts with the engine off.

a) Calculate the magnitude of the acceleration of the car during the first 50 m.
A) 1.2 m/s²
B) 3.4 m/s²
C) 6.8 m/s²
D) 8.0 m/s²

Answer 1

The magnitude of the car's acceleration during the first 50 m is 2.89 m/s², which is not present in any of the given options.

Step-by-step explanation:

To calculate the magnitude of the acceleration of the car during the first 50 m, we must use the kinematic equation that relates acceleration, distance, initial velocity, and final velocity: v2 = u2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance traveled. Given that the car starts from rest, u = 0, and the speed v when the car reaches the beginning of the hill is 17 m/s after covering a distance s of 50 m. Substituting these values into the equation yields:

172 = 0 + 2 × a × 50,

289 = 100a,

a = 2.89 m/s2.

The correct answer is not listed as an option because the calculation results in 2.89 m/s2, not any of the provided options (A) 1.2 m/s2, (B) 3.4 m/s2, (C) 6.8 m/s2, or (D) 8.0 m/s2.