Question

A North-South road meets an East-West road at an intersection. At a certain moment, a car on the North-South road is 4 miles north of the intersection and is traveling north at 55 miles per hour. At the same moment, a truck on the East-West road is 3 miles east of the intersection and is traveling east at 45 miles per hour. How fast is the distance between the car and the truck increasing at that moment?

Answer 1

Answer:

The distance 5 miles North-East of the intersection between the car and the truck increasing at 71.06 miles per hour at that moment.

Step-by-step explanation:

Looking at the attached figures, Fig 1 shows the diagram of the car and the truck.

Using Pythagoras theorem on Fig 1a,

$l^{2} = \sqrt{3^{2} + 4^{2} }$

$l = \sqrt{9 +16} \\\\l= \sqrt{25} \\\\l = 5 miles$

The resultant displacement between the car and the truck at that same moment is 5 miles.

From the velocity vector diagram on Fig 2,

The resultant velocity R is given as

$R = \sqrt{45^{2} + 55^{2} }\\\\R = \sqrt{2025 + 3025 }\\\\R = \sqrt{5050 }\\\\R = 71.06mph$

Therefore, the distance 5 miles North-East of the intersection between the car and the truck increasing at 71.06 miles per hour at that moment.