Question

a bicyclist is riding on a road next to a train. the train is traveling to the right at 45m/s (relative to the earth) and the bicyclist is traveling to the left at 13m/s (relative to the earth). from the perspective of the bicyclist, what is the trains speed and direction? m/s,

Explanation:

Step1: Define velocity directions

Let the right - hand direction be positive. The train's velocity relative to the earth $v_{t - e}=45m/s$, and the bicyclist's velocity relative to the earth $v_{b - e}=- 13m/s$.

Step2: Use relative - velocity formula

The formula for relative velocity is $v_{t - b}=v_{t - e}-v_{b - e}$.
Substitute the values: $v_{t - b}=45-(-13)$.

Step3: Calculate the result

$v_{t - b}=45 + 13=58m/s$. Since the result is positive, the direction is to the right.

Answer:

58, right