Two Cars Approaching An Intersection?

Question

Two cars are approaching an intersection. One is 4 miles south of the intersection and is moving at a constant speed of 50 miles per hour. At the same time, the other car is 5 miles east of the intersection and is moving at a constant speed of 60 miles per hour.

(a) Express the distance d between the cars as a function of time t.

HINT GIVEN: At t = 0, the cars are 4 miles south and 5 miles east of the intersection, respectively.

Sorry, but this hint does not make sense to me. I need someone to solve this question step by step explaining as you go through the problem. Okay?

Answer 1

The cars form a right triangle with the interesection at the vertex between the two legs and the hypotoneus being the distance between the two cars.

Initially the distance is: sqrt(4^2+5^2) = 6.4 miles

Now let the south car have a speed vs and let the distance from the intersection be 4-y. Now y = vs*t where t = time

Let the east car have a speed ve and let the distance from the intersection be 5-x. x = ve*t

The distance between the cars is:

d(t) = sqrt((5-ve*t)^2 +(4-vs*t)^2)

= sqrt(25 - 10ve*t +(ve*t)^2 + 16 - 8vs*t +(vs*t)^2)

= sqrt(41 - (10ve + 8vs)*t +(ve^2+vs^2)*t^2))

= sqrt(41 - 1000*t + 6100*t^2) (plugged in the numbers for the speed of the east car (ve) and south car (vs))

Note when t = 0, d(0) = sqrt(41) = 6.4 miles.

Answer 2

t=0 cars are 4 mile south and 5 miles east
t+1 cars are how far south and east ( bit less, 60mph for 1 sec and 50mph for 1 sec)
t+2 cars are how far.....etc
t+x cars smash into each other or miss and are north and west of the junction

Answer 3

Distance = √ ( 4 -50t)²+(5-60t)²
Distance = √( (16 -400 + 2500t² ) + ( 25 -600t+3600t²) )
Distance = √ ( 41 - 1000t + 6100t² )

Answer 4

the motor vehicle on the marvelous has the marvelous-of-way, yet while i exchange into on the marvelous i might extremely be watching to make certain if the motor vehicle on the left is going to offer up. i does not anticipate considering the fact that I had the marvelous-of-way that he will supply it to me.

Answer 5

d=root(25t^2 - 46t + 21)