For a particular stretch of highway illuminated by a row of identical lamps, measurements show that at every moment the length s (in metres) of a car’s shadow is 1.6 times the car’s distance d (in metres) from the base of the nearest lamp. A car 1.4m tall travels straight away from that lamp at a constant 22ms−1.
(a) Using the relationship s=1.6d, find dtds while the car is in motion. Give units.
(b) Determine the speed of the tip of the car’s shadow at that same moment and express your answer with appropriate units.