(Use decimal notation. Give your answer to three decimal places.) The rate of ch

Question

(Use decimal notation. Give your answer to three decimal places.)

The rate of change of the distance between the vehicles is _______km/hr

A police car is traveling south on Hwy 43 toward Sioux City at 180 km/h and a truck is traveling east away from Sioux City, IA, at 120 km/h (See figure below). At time t_0=0, the police car is 60 km north and the truck is 60 km east of Sioux Falls. Calculate the rate at which the distance between the vehicles is changing after 5 minutes. (Use decimal notation. Give your answer to three decimal places.) The rate of change of the distance between the vehicles is _______km/hr

Explanation / Answer

initial distance = sqrt ( 60^2 + 60^2 ) = 60 *sqrt (2) = 84.84 km and after 5 min means 1/12 hours police car travelled = 1/12 * 180 = 15 km and truck = 1/12 * 120 = 10 km so now distance of car from sioux falls = 60 -15 =45 km and truck = 60 + 10= 70km so now distance between car and truck = sqrt( 45^2 + 70^2) = 83.22 km so rate of change = (84.84 -83.22) / (1/12) = 19.44 km /hr

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