A rod 10 ft moves with its ends A and B on two perpendicular lines OX and OY respectively - Maths - Application of Derivatives

Question

A rod 10 ft moves with its ends A and B on two perpendicular lines
OX and OY respectively If A moves at the rate of 2 ft/sec when it
is 8 ft from O, find at what rate, end B is moving

Varun.Rawat · Accepted Answer

Let x be the distance covered by end A along OX and y by end B along OY at any instant t
Length of the rod = 10 ftIn ∆AOB,OA2 + OB2 = AB2  Pythagoras theorem⇒102 = y2+x2⇒x2+y2 = 100    
1Differentiating both sides with respect to t, we get    2xdxdt + 2ydydt = 0⇒xdxdt + ydydt = 0   ⇒x × 2 + ydydt = 0    as, dxdt = 2 ft/s⇒dydt = -2xyWhen x = 8, then from 1, we get y = 6
Now, dydt = -2 × 86 = -83 ft/sSo, end B is moving with the speed of  -83 ft/s

A rod 10 ft. moves with its ends A and B on two perpendicular lines OX and OY respectively. If A moves at the rate of 2 ft/sec when it is 8 ft. from O, find at what rate, end B is moving.