Question

A motorcycle patrolman is monitoring traffic from behind a billboard along a stretch of road where the speed limit is 96.0 km/hr. He clocks a motorist at 107 km/hr and decides to give chase and award the driver a speeding ticket. By the time he gets onto the highway and up to his chase speed of 131 km/hr, he is 350 m behind the speeder. Determine the amount of time it takes the patrolman to catch the speeder.

Answer 1

The time taken is
`t = 52.5 \ s`

Step-by-step explanation:

From the question we are told that

The speed limit is
`v__{{l}}} = 96.0 \ km/hr = (96 * 1000)/(3600) = 26.7 \ m/s`

The velocity of the motorist is
`v_m = 107 \ km/hr = (107 * 1000)/(3600) = 29.72 \ m/s`

The chase speed of the motorcycle patrolman is
`v = 131 \ km/hr = (131 *1000)/(3600) = 36.39 \ m/s`

The relative distance between the motorcycle patrolman and the speeder is d= 350 m

Generally the relative speed between the the motorcycle patrolman and the speeder is mathematically represented as

`v_r = v - v_m`

=>
`v_r = 36.39 - 29.72`

=>
`v_r = 6.67 \ m/s`

Generally the time taken is mathematically represented as

`t = (v_r)/(d)`

=>
`t =  (350)/( 6.67)`

=>
`t =  52.5 \  s`