13. A car traveling at 60 km/h will skid 30 m when its brakes are locked. If the same care is traveling at 180 km/h, what will be the skidding distance? Be sure to show all work to support your answer.
triple the speed, increase distance by 9x
distance=9*30
reason:
work done=KE
friction*distance=1/2 m v^2
so distance is proportional to v^2
since the distance is proportional the the square of the speed,
3*speed ==> 9*distance
Interesting, how showing your work means showing the work!
To find the skidding distance at 180 km/h, we can use the concept of proportion.
Given:
Speed of the car = 60 km/h
Skidding distance at 60 km/h = 30 m
First, let's find the distance covered by the car in one hour at 60 km/h:
Distance covered = Speed × Time
Distance covered = 60 km/h × 1 h = 60 km
We know that the skidding distance is 30 m, which is equivalent to 0.03 km.
Now, we can set up a proportion to find the skidding distance at 180 km/h:
(skidding distance at 60 km/h) / (distance covered at 60 km/h) = (skidding distance at 180 km/h) / (distance covered at 180 km/h)
Substituting the given values:
30 m / 0.03 km = (skidding distance at 180 km/h) / (60 km/h × 3 h)
We need to convert the skidding distance and distance covered at 180 km/h to meters:
180 km/h = 180,000 m/3,600 s = 50 m/s
60 km/h × 3 h = 60 km/3600 s = 16.67 m/s
Substituting the converted values into the proportion:
30 m / 0.03 km = (skidding distance at 180 km/h) / (16.67 m/s × 3 s)
30 m / 0.03 km = (skidding distance at 180 km/h) / (50 m/s × 3 s)
Now, let's solve for the skidding distance at 180 km/h:
(30 m / 0.03 km) × (50 m/s × 3 s) = skidding distance at 180 km/h
(30 × 500 × 3) / 3 = skidding distance at 180 km/h
(4500) / 3 = skidding distance at 180 km/h
1500 m = skidding distance at 180 km/h
Therefore, the skidding distance for the car traveling at 180 km/h will be 1500 meters.