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?

1 Answer
Nov 9, 2015

Answer:

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#