A 2.5 ton truck stops and a 1300 pound car slams the brakes and skids 26 feet and hits the truck at 40 mph pushing the truck a foots length. how fast was the 1300 pound car traveling?
To calculate the speed at which the 1300 pound car was traveling, we can follow these steps:
Step 1: Convert the weight of the truck from tons to pounds.
Given that the truck weighs 2.5 tons, we can multiply this value by 2000 (since 1 ton equals 2000 pounds) to convert it to pounds:
2.5 tons * 2000 pounds/ton = 5000 pounds
Step 2: Convert the length skidded by the car from feet to miles.
The car skidded 26 feet, so we need to convert this to miles. Since 1 mile equals 5280 feet:
26 feet / 5280 feet/mile ≈ 0.004924 miles
Step 3: Convert the foots length to feet.
Given that the car pushed the truck a "foot's length," we consider this as one foot.
Step 4: Calculate the change in momentum of the truck.
The change in momentum can be calculated using the formula:
Change in momentum = (Mass of truck * Final speed of truck) - (Mass of truck * Initial speed of truck)
Given:
Mass of truck = 5000 pounds
Final speed of truck = Initial speed of truck (since it stopped)
Change in momentum = (5000 pounds * 0 mph) - (5000 pounds * Initial speed of truck)
Step 5: Calculate the change in momentum of the car.
The change in momentum can be calculated using the formula:
Change in momentum = Mass of car * Final speed of car - Mass of car * Initial speed of car
Since the car initially skidded and then hit the truck, its final speed is 0 mph.
Change in momentum = (1300 pounds * 0 mph) - (1300 pounds * Initial speed of car)
Step 6: Set the change in momentum of the truck equal to the change in momentum of the car, solve for "Initial speed of car."
(5000 pounds * 0 mph) - (5000 pounds * Initial speed of truck) = (1300 pounds * 0 mph) - (1300 pounds * Initial speed of car)
(5000 pounds * Initial speed of truck) = (1300 pounds * Initial speed of car)
Step 7: Solve for "Initial speed of car."
Initial speed of car = (5000 pounds * Initial speed of truck) / 1300 pounds
Step 8: Convert the initial speed of the car from mph to feet per second.
Since we need to compare the speed of the car to the length of the skid, we should express both in consistent units.
1 mile/hour = 1.47 feet/second (approximately)
Initial speed of car (in feet/second) = Initial speed of car (in mph) * 1.47 feet/second
By following these steps and plugging in the relevant values, you can find the speed at which the 1300 pound car was traveling before hitting the truck.