You're on a train that is moving at 160 km/h and decide to run
towards the rear of the railroad car. The length of the car is 18 m
and it takes you 5.0 s to go from the front to the back of the car.
What is your speed relative to the tracks?
train speed = 160000 m / 3600 s
run speed = 18 m / 5.0 s
speed relative to the tracks = train speed - run speed
To find your speed relative to the tracks, we need to first find your speed while running inside the train car, and then add it to the speed of the train.
Step 1: Convert the length of the car to kilometers.
The length of the car is given as 18 m. To convert it to kilometers, divide it by 1000:
18 m / 1000 = 0.018 km
Step 2: Convert the time to hours.
The time taken to go from the front to the back of the car is given as 5.0 s. To convert it to hours, divide it by 3600:
5.0 s / 3600 = 0.00139 hours
Step 3: Calculate your speed inside the car.
To find your speed inside the car, divide the distance you covered by the time taken:
0.018 km / 0.00139 hours = 12.95 km/h (rounded to two decimal places)
Step 4: Calculate your speed relative to the tracks.
To find your speed relative to the tracks, add your speed inside the car to the speed of the train:
12.95 km/h + 160 km/h = 172.95 km/h (rounded to two decimal places)
Therefore, your speed relative to the tracks is approximately 172.95 km/h.
To determine your speed relative to the tracks, we need to consider both your speed running inside the train and the speed of the train itself.
Given:
- Speed of the train: 160 km/h
- Length of the car: 18 m
- Time taken to go from the front to the back of the car: 5.0 s
First, let's convert the train's speed from kilometers per hour to meters per second.
Step 1: Convert the train's speed from km/h to m/s:
160 km/h = (160 * 1000 m) / (60 * 60 s) = 44.44 m/s
Now, let's calculate your speed relative to the tracks.
Step 2: Determine the distance you moved while running inside the train:
Distance = Length of the car = 18 m
Step 3: Convert the distance you moved from meters to kilometers:
Distance = 18 m = 0.018 km
Step 4: Calculate your speed running inside the train:
Speed = Distance / Time
Speed = 0.018 km / 5.0 s
Step 5: Convert your speed from kilometers per second to meters per second:
Speed = (0.018 km / 5.0 s) * (1000 m / 1 km) = 3.6 m/s
Step 6: Calculate your speed relative to the tracks by adding your running speed to the train's speed:
Speed relative to tracks = Train's speed + Your speed
Speed relative to tracks = 44.44 m/s + 3.6 m/s
Step 7: Calculate the final result:
Speed relative to tracks = 48.04 m/s
Therefore, your speed relative to the tracks is 48.04 m/s.