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A helicopter flies parallel to the ground at an altitude of 1/2 kilometer and at a speed of 2 kilometers per minute. If the helicopter passes directly over the White House, at what rate is the distance between the helicopter and the White House changing 1 minute after the helicopter flies over the White House?1 minute after the helicopter passes over the White House, its distance from the White House is changing at a rate of ______ kilometers per minute.

Question

A helicopter flies parallel to the ground at an altitude of 1/2 kilometer and at a speed of 2 kilometers per minute. If the helicopter passes directly over the White House, at what rate is the distance between the helicopter and the White House changing 1 minute after the helicopter flies over the White House?

1 minute after the helicopter passes over the White House, its distance from the White House is changing at a rate of ______ kilometers per minute.

check_circleAnswer
Step 1

The numerical can be constructed as shown below,
let H be the altitude = 0.5 km

         V be the speed =2 km/min


The horizontal distance z travelled at the end of 2 minutes will be 2km/min* 2 min=4 kms

V 2km/min
Z
H 0.5 km
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V 2km/min Z H 0.5 km

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Step 2

Let the distance from the white house be given by the red line denoted by X. It can be expressed in terms of V and H as,

Using Pythag oras Therorem
Taking derivative on both sides with respect to time,
d
d
(x2)(Z2)+(H2
dt
dt
)
dt
Since altitute does not vary with time, (H2) 0
dt
2X(X
dt
2Z-- (Z) 0
dt
(X)= z(z)
X
dt
Z
dt
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Using Pythag oras Therorem Taking derivative on both sides with respect to time, d d (x2)(Z2)+(H2 dt dt ) dt Since altitute does not vary with time, (H2) 0 dt 2X(X dt 2Z-- (Z) 0 dt (X)= z(z) X dt Z dt

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Step 3

Substitute the values an...

X(X 4.2
dt
- (X)
dt
X
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X(X 4.2 dt - (X) dt X

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Tagged in

Math

Calculus

Derivative

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