A light shines from the top of a pole 5 m high. A ball is dropped from a point 4 m away from the pole. Find how fast the shadow of the ball is moving when the ball is 2 m above the ground and moving at a speed of 9 m/sec.
(Bilkent University, 1st Midterm Question)
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Finding the equation of x and y
y 5 = x x + 4 thus x = 5 − y 4 y
Derivating x regarding to time using quotient rule
d t d x = ( 5 − y 4 + ( 5 − y ) 2 4 y ) d t d y
Thus at the moment when y = 2 m and d t d y = 9 m / s e c
d t d x = ( 5 − 2 4 + ( 5 − ) 2 4 . 2 ) . ( − 9 ) = − 2 0 m / s e c
The shadow of the ball is moving at a speed of -20 m/sec at this moment