Question

a van starts off 189 miles directly south from the city of hartville. it travels due west at a speed of 30 miles per hour. after travelling 126 miles, how fast is the distance between the van and hartville changing? (do not include units in your answer, and round to the nearest hundredth.)

Answer 1

The rate at which the distance between the van and Hartville is changing is 15 miles per hour.

Step-by-step explanation:

To find the rate at which the distance between the van and Hartville is changing, we can use the concept of relative velocity. Since the van is traveling due west, we can consider the distance between the van and Hartville as the horizontal component of the displacement between the two points. The horizontal displacement is given by the difference between the initial position (189 miles south of Hartville) and the current position (126 miles west of the initial position). So, the horizontal displacement is 189 - 126 = 63 miles.

To find the rate at which the distance is changing, we need to consider the speed at which the van is moving westward. The van is traveling at a speed of 30 miles per hour. Therefore, the rate at which the distance is changing is the horizontal displacement divided by the time taken. Since the van has traveled 126 miles in the westward direction, the rate at which the distance between the van and Hartville is changing is 63 miles / (126 miles / 30 miles per hour) = 15 miles per hour.