Question

An automobile traveling at a rate of 30 ft/sec is approaching an intersection. When the automobile is 120 ft 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 each other. How fast are the automobile and the truck seperating 2 sec after the truck leaves the intersection?

Answer 1

Answer:

14ft/sec

Step-by-step explanation:

GIVEN:  An automobile traveling at a rate of 30 ft/sec is approaching an intersection. When the automobile is 120 ft from the intersection, a truck traveling at the rate of 40 ft/sec crosses the intersection.

IN SKETCH BELOW............. IN THE ATTACHMENT

A IS AUTOMOBILE AND V IS TRUCK AT TIME T= 0

TRUCK IS AT M AFTER T SECONDS...AUTOMOBILE IS AT L AFTER T SECS.

AT=120 '

After T seconds

AL= 30T

LV= 120-30T

VM= 40T

LM = $\sqrt{(120-30T)^2+40T^2}$ ( let this be s)

now , ds/dt = $\sqrt{\frac{2(-30)(120-30T)+3200T}{2\sqrt{(120-30T)^2+1600T^2} } }$

$\frac{ds}{dt} = \frac{2500T-3600}{\sqrt{(120-30T)^2+1600T^2} }$

now in this equation put T=2 we get

$\frac{5000-3600}{\sqrt{3600+6400} }$

ds/dt= 1400/100= 14 FPS

hence the two vehicles are separating at 14 ft/sec at T=2 seconds