Final answer:
Given the increased apparent weight of a person in the car, we can calculate the car's speed using the formula for centripetal force. Applying the concept that the apparent weight is 1.80 times the normal weight, and substituting known values for gravity and the radius of the circular path, the car's speed is found to be 8.4 m/s at the bottom of the hill.
Step-by-step explanation:
The student is asking about the speed of a car traveling at the bottom of a 9.00-meter-radius circular hill. Given that a person sitting on a scale in the car reads a value that is 80% more than their normal weight, we can deduce that the normal force exerted by the scale is significantly higher due to the centripetal acceleration required to keep the car moving in a circle at the bottom of the hill.
To find the speed v of the car, we use the concept of circular motion and the apparent weight increase due to the centripetal force. The physics formula that relates force, mass, and acceleration is F = ma, where F is the force, m is the mass, and a is the acceleration. Since the person's apparent weight is 80% more than their normal weight, we can write the equation for the apparent weight (W') as:
W' = W + Fc
where W is the normal weight, and Fc is the centripetal force, which is m * ac (with ac being the centripetal acceleration). Given that the apparent weight is 1.80 times the normal weight, we can set up the following equation:
1.80W = W + m * (v2 / r)
Solving for v, we get:
v = sqrt((1.80 - 1) * g * r)
Substituting the given values g = 9.80 m/s2 and r = 9.00 m, we find:
v = sqrt(0.80 * 9.80 m/s2 * 9.00 m)
After calculations, we get:
v = 8.4 m/s
Therefore, the car is traveling at a speed of 8.4 meters per second (m/s) when the scale reading increases by 80% at the bottom of the hill.