.....Mechanicsl

Question

A speeding boda boda cyclist rides through 50 km/he zone at 70 km/he without noticing a stationery police patrol pick up. The patrol officer immediately heads after the boda boda cyclist, accelerating at 90 km/hr/s when the officer pulls a long side the rider, how far down the road are they, how long does it take the patrol to catch up with bike and how fast is the police car going.

Answer 1

This is a typical pursuit problem except it is simplified by not having some sort of delay which would require adjustment of the equations of motion. In this case you can just write the equations for the movement of the cyclist (c) and the police car (p) and find the time when they have gone the same distance:

constant v cyclist: d = v₀t = (70km/hr)(1hr/3600s) * t with t in seconds (v in km/s)

constant a police car d = (1/2)at² = (1/2)*(90km/hr-s)(1hr/3600s) t² with t in seconds (a in km/s²)

70t = (1/2)(90)t² (The seconds correction cancels, but still necessary in next step)

t = (70/45) seconds

You can find the correct distance by plugging into either equation listed (must have the conversion in it or convert to hours and pulg into the constant velocity equation.

Please consider a tutor. Take care.