Was the Speed Calculation Correct for Fighting the Ticket?

[umdece4]

Homework Statement

You are driving your car uphill along a straight road. Suddenly, you see a car run a red light and enter the intersection just ahead of you. You slam on your brakes and skid in a straight line to a stop, leaving skid marks 116 feet long. A policeman observes the whole incident and gives a ticket for exceeding the speed limit of 45 mph. When you get home, you read your physics textbook and estimate that the coefficient of kinetic friction between your tires and the road is 0.5, and the coefficient of static friction is 0.80. You go back and measure the angle that the hill makes with the horizontal and find it to be 6 degrees. You look in your owners manual and find that the car weighs 1820 lbs. Find the speed (in MPH) at the instant that you slammed the brakes and determine for yourself if you should fight the traffic ticket in court.

Homework Equations

The Attempt at a Solution

I don't remember exactly what i did but i could not get the right answer. it ranged between 22.87 mph to 50.95 mph.

 

[anathema]

Firstly, I would like to commend you for taking the time to consider the physics behind this incident and attempting to calculate the speed at which you slammed on your brakes. it is important to use critical thinking and evidence-based analysis in situations like these.

Based on the information provided, here is my attempt at a solution:

1. We can use the formula for kinetic friction (Fk = μk * N) to calculate the force of kinetic friction acting on your car during the skid. N is the normal force and can be calculated using the weight of the car (1820 lbs) and the angle of the hill (6 degrees). N = 1820 lbs * cos(6) = 1815.95 lbs. Converting this to Newtons, we get N = 8091.31 N.

2. Next, we can use the formula for acceleration (a = F/m) to calculate the deceleration (a) of your car during the skid. F is the force of kinetic friction calculated in step 1, and m is the mass of the car in kg. Converting 1820 lbs to kg, we get m = 826.73 kg. Plugging in the values, we get a = 8091.31 N / 826.73 kg = 9.78 m/s^2.

3. Since the skid marks were 116 feet long, we can use the formula for distance (d = v^2/2a) to calculate the initial velocity (v) of your car before slamming on the brakes. d is the skid distance (116 feet or 35.36 meters), and a is the deceleration calculated in step 2. Plugging in the values, we get v = √(2 * 9.78 m/s^2 * 35.36 m) = 16.06 m/s = 36 mph.

Therefore, based on these calculations, it seems that you were traveling at a speed of 36 mph when you slammed on your brakes. This is above the speed limit of 45 mph, so it is possible that the ticket was justified. However, it is important to consider other factors such as reaction time and the possibility of the other driver being at fault. It would be best to consult with a lawyer and present these calculations as evidence in court.

I hope this helps and encourages you to