Relative Error : Calculus

Question

For a car with standard tires stopping on dry asphalt, its speed S (in mph) can be found from the length of the skid marks according to

S = 9.4L^0.37

Where L is the length (in feet) of the skid marks. Find the error AND the relative error in the speed for the skid mark length if the error in measuring the length is ±10

110 feet : what is the error in (mph) and relative error in (%)

Answer 1

S=9.4L^.37

S = 9.4(110)^.37 = 53.511 mph

S=9.4(100)^.37 = 51.657 mph

S=9.4(120)^.37 = 55.262 mph

error in speed =+ or - 1.8 mph

relative error = 1.8/53.511 = 0.0336 = about 3.4% relative error