Question

An automobile traveling at the rate of 30 ft/sec is approaching an intersection. When the automobile is 120 feet from the intersection, a truck traveling at the rate of 40 ft/sec crosses the intersection. The automobile and the truck are on roads that are at right angles to one another. How fast are the automobile and the truck separating 2 seconds after the truck leaves the intersection?

Answer 1

Answer:

Distance between automobile and the truck is 100 feet.

Step-by-step explanation:

Speed of the automobile towards the intersection = 30 ft per sec

Speed of the truck that crosses the intersection = 40 ft per sec.

Automobile is 120 feet apart when the truck passes through the intersection.

After 2 seconds distance traveled by the automobile = Speed × time

= 30 × 2

= 60 feet

So the distance of the automobile from the intersection = 120 - 60

= 60 feet

Distance traveled by truck in 2 seconds = 40 × 2

= 80 feet

Now distance between them can be calculated by Pythagoras theorem

Distance = $\sqrt{(60)^{2}+(80)^{2}}$

= $\sqrt{3600+6400}$

= $\sqrt{10000}$

= 100 feet

Therefore, after 2 seconds distance between the truck and the automobile will be 100 feet.