Consider the freight train in Figure below. Suppose 17 boxcars pass by in a time of 10.7 s and each has a length of 15.3 m. (a) What is the frequency at which each boxcar passes? (b) What is the speed of the train?
what is the time for each boxcar?
17/10.7
what is the frequency (hint 1/time)
speed= lengthboxcar*frequency
To find the frequency at which each boxcar passes, we need to calculate the number of boxcars passing per unit time.
Given:
Time taken for 17 boxcars to pass = 10.7 s
Length of each boxcar = 15.3 m
(a) Frequency:
Frequency is defined as the number of events occurring per unit time.
Number of boxcars passing = 17
Time taken = 10.7 s
Frequency is calculated using the formula:
Frequency = Number of events / Time taken
Frequency = 17 / 10.7
Frequency = 1.59 Hz
Therefore, the frequency at which each boxcar passes is approximately 1.59 Hz.
(b) Speed of the train:
Speed is defined as the distance traveled per unit time.
Total distance traveled by the train is the total length covered by the boxcars passing.
Number of boxcars passing = 17
Length of each boxcar = 15.3 m
Total distance traveled = Number of boxcars passing × Length of each boxcar
Total distance traveled = 17 × 15.3
Total distance traveled = 260.1 m
Time taken = 10.7 s
Speed is calculated using the formula:
Speed = Distance / Time
Speed = 260.1 / 10.7
Speed ≈ 24.25 m/s
Therefore, the speed of the train is approximately 24.25 m/s.
To answer these questions, we need to first calculate the time it takes for a single boxcar to pass and then use that information to find the frequency and speed of the train. Here's the step-by-step process:
(a) To find the frequency at which each boxcar passes, we need to calculate the time it takes for a single boxcar to pass. We can do this by dividing the total time taken for 17 boxcars to pass by the number of boxcars. In this case:
Time taken for 1 boxcar to pass = Total time taken for 17 boxcars to pass / 17
= 10.7 s / 17
(b) Once we have the time taken for one boxcar to pass, we can calculate the speed of the train. The speed of the train is equal to the length of one boxcar divided by the time taken for that boxcar to pass. In this case:
Speed of the train = Length of one boxcar / Time taken for one boxcar to pass
Now, let's substitute the values and calculate:
Speed of the train = 15.3 m / (10.7 s / 17)
To simplify this equation, we need to divide 10.7 s by 17:
Speed of the train = 15.3 m / (10.7 s / 17)
= 15.3 m / (0.6294 s)
Finally, we can calculate the speed:
Speed of the train = 15.3 m / 0.6294 s
Now, let's compute the value.