Question

Your friend is traveling at a constant 30.0m/s and has a 1600m head start. How many minutes will it take you to catch them if you are traveling at a constant 50.0m/s?

Answer 1

80 seconds

Explanation:

By defining `t` as the time it will take to you and your friend to be in the same position `x`; `x_0` is the starting position and using the equation of motion `x=x_0 + vt` you have:
`x = 1600 + 30*t`
`x = 0 + 50*t`
Since you want the moment when both are in the same position, that is the same `x`, you make both equations equal.
`1600 + 30*t = 50*t`
And solving for `t` to know the time:
`t = (1600 m)/(50 m/s -30 m/s) = (1600 m)/(20 m/s) = 80 s`