Trisha and Gordon drive away from a campground at right angles to each other. Trisha's speed is 70mph and Gordon's speed is 55mph. Express the distance between the cars as a function of time.
First, we need to determine the distance each travel. Since we aren't sure how long that is, we use:
t = time travelled in hours
You can assume they started travelling at the same time. So, the distance one travels would be:
D1 = v1t
D1 = 70t
And, for the other one:
D2 = 55t
When we lay these out on paper, we would have a right triangle. And, the problem would be asking us to find the hypotenuse. So, we would have:
D = √(D12 + D22)
D = √((70t)2 + (55t)2)
D = √(4900t2 + 3025t2)
D = √(7925t2)
So, D would be (√7925)t, or approximately 89.02t.
Good luck, Iro1979. I hope this helps.
You need to use distance equation such that:
`v = d/t => d = v*t`
`v` represents the velocity
`d` represents the distance between cars
You need to evaluate the velocity using the information provided by the problem, such that:
`v = sqrt(v_x^2 + v_y^2) => v = sqrt(55^2 + 70^2)`
`v = sqrt(3025 + 4900) => v = sqrt(7925)`
`f(t) = sqrt(7925)*t`
Hence, expressing the distance between cars as a function of time yields `f(t) = sqrt(7925)*t.`