Hi, if x is how far the plane moves, x is v_{p}t and dx/dt is v_{p}^{ }(Note, you have to convert km/hr to km/s by dividing by 3600)

The distance away from the radar is s = sqrt((8km)^{2}+ x^{2}) (just the hypotenuse of right triangle formed by altitude and x)

It's actually easier to implicitly differentiate s^{2} = 64 + x^{2}

2s ds/dt = 2x dx/dt

ds/dt = (x/s) dx/dt (ds/dt is what the question is asking)

At t = 36 s, x = v_{p}t, s = sqrt(64 + x^{2}), and dx/dt = v_{p}

I hope that helped!

JACQUES D.

09/15/20

Kate B.

Okay, so to solve for x, I just divide the 600km by 3600 and multiply that number by 36 seconds? Or am I interpreting that wrong. Everything else you said I already had, which is reassuring!!09/15/20