A car is travelling along the road where the speed limit is 30 mph. A speed detector measures it speed as 15 m/s. Use this fact to work out whether or not the car is breaking the speed limit: there are 1609 m in a mile

The speed of the car is in from as the required speed limit on the road.

Explanation:

The speed limit on the road is 30 miles per hour.

Given that: 1 mile = 1609 m

Also,

60 second = 1 minutes

60 minutes = 1 hour

Then,

30 miles per  hour =

                              =

                              = 13.4083

30 miles per  hour  = 13.41 m/s

The speed measured by the detector is 15 m/s which is not accurate. Therefore, the car was moving at the required speed limit. The speed of the car is lesser than that measured by the detector. Thus no offence has been committed by the driver.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west