Question

Calculus HELP PLEASE? A highway runs due north. A car traveling at 50 mph exits the highway at a 30° angle. After driving another 1.5 hours at the same speed and direction, how far away is the car from the highway?

Answer 1

check the picture below.

notice that the car exits the northbound highway, and whilst going at 50mph for 1.5 hours, that simply means going for 75 miles.

make sure your calculator is in Degree mode.

Answer 2

37.5 miles is the answer.

Explanation:

Since car is travelling with a speed = 50 mph

Angle between the highway and the track on which the car is travelling = 30°

Now we know sin∅ = distance between highway and the car/Distance traveled by the car on the new track

Distance traveled by the car in 1.5 hours = speed × time

= 50 × 1.5 = 75 mi.

Therefore sin 30° = x/75

x = 75×sin30° = 75 × 1/2 = 37.5 mi.

Therefore the answer is 37.5 mi away.