Answer:
The distance between the helicopter and the man changing at that instant is 41.46 ft/sec.
Explanation:
Given:
Distance between the man and the helipad, = ft
Vertical distance between the helipad and the helicopter, = ft
Helicopter lift off vertically and is raising at a speed of 45 ft/sec.
That can be written as, = 45 ft/sec
Now from the diagram (attached with) we can find the hypotenuse of the triangle that is the distance between the man and the helicopter.
Applying Pythagoras theorem:
⇒
⇒
⇒
⇒ ft
Now to find the changing distance between the helicopter and the man we have to differentiate the Pythagoras theorem as dh/dt can be obtained from there.
And we know that the distance b is constant so db/dt=0.
Using chain rule and power rule of differentiation.
⇒
⇒
⇒
⇒ <em>....eliminating the common 2 </em>
⇒
⇒ Plugging the values.
⇒
⇒ ft/sec
So,
41.46 ft/sec is the distance between the helicopter and the man changing at that instant.