Question

1. A helicopter spraying fertilizer over a field can fly 5 miles downhill in the same time as it can fly 4 miles upwind. Find the speed of the wind if the helicopter travels 45 mph in still air when dusting crops.

2. The illumination provided by a car's headlight varies inversely as the square of the distance from the headlight. A car's headlight produces an illumination of 3.75 footcandles at a distance of 40 feet. What is the illumination when the distance is 60 feet?

Answer 1

1. Let the speed of the wind be x mph. Then the speed of the helicopter upwind is 45-x mph and its speed downwind is 45+x mph.

Since time = distance/speed,and since the helicopter can fly 5 miles downhill in the same time as it can fly 4 miles upwind, hence 5/(45+x) = 4/(45-x) or, 5(45-x)= 4(45+x) or, 225-5x = 180+4x or, 9x = 225-180 = 45 so that x = 45/9 = 5. Hence the speed of the wind is 5 mph.

2. Let k be the constant of proportionality. Since the illumination provided by a car's headlight varies inversely as the square of the distance from the headlight and since the car's headlight produces an illumination of 3.75 foot candles at a distance of 40 feet , hence 3.75 = k*(1/40)² = k/1600 so that k = 1600*3.75 = 6000. Now, when the distance is 60 feet, the illumination will be k/(60)² = 6000/3600 = 1.67 foot candles ( on rounding off to 2 decimal places).