00:01
Okay, the two roads then meets here and your toe, that's perpendicular.
00:07
And a is north on that point and travelling south at 55 miles per hour.
00:13
So here is car a going south.
00:16
Car b is east of the point over here and travelling west towards the point at 35 miles per hour.
00:25
So i suppose then at this distance vertically is y.
00:33
Miles and distance here is x miles and a and b the gap is z miles so x y and z here all changing now what connects x y and z well pythagoras this triangle is right angle so i have x squared plus y squared equals z squared now, i want to work out rate of change of z.
01:06
So that means what i would do, i would differentiate both sides.
01:11
I would take d by dt of the left and d by dt of the right.
01:18
It's implicit.
01:20
So what happens is i do it as normal.
01:23
So i do 2x and then put at the end of it, dx by dt.
01:29
Likewise, y square becomes 2y.
01:33
Dy by dt and z square becomes 2z dz by dt.
01:43
Then the two is all cancelate...