Question
Asked Oct 16, 2019

A weather balloon is rising vertically at the rate of 10ft/s. An observer is standing on the ground 300 ft, horizontally from the point where the balloon was released. At what rate is the distance between the observer and the balloon changing when the balloon is 400ft high?

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Step 1

Given: -

The rate at which balloon rises vertically 10 ft / sec
Distance between observer and the point from where balloon released =
300 ft
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The rate at which balloon rises vertically 10 ft / sec Distance between observer and the point from where balloon released = 300 ft

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Step 2

To find: -

Rate at which distance between the observer and the balloon changing
when the balloon is 400ft high.
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Rate at which distance between the observer and the balloon changing when the balloon is 400ft high.

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Step 3

Calculation...

The rate at which position of the balloon at a time t is given by
y = o+ v,t
It is given that initially the balloon is at ground level,
the distance between balloon and observer is:
d()(300 f[(10 ft / see)t
Differentiating both the sides with respect to time 't
d()(300[0/sec)T)
d
2 (d(t)(300ft +10 ft /sec-
dt
dt
dt
2d (t)d'(t) 0+10 ft / secx 2t
10 ft/secxt
d'(t)
-(1)
d(t)
help_outline

Image Transcriptionclose

The rate at which position of the balloon at a time t is given by y = o+ v,t It is given that initially the balloon is at ground level, the distance between balloon and observer is: d()(300 f[(10 ft / see)t Differentiating both the sides with respect to time 't d()(300[0/sec)T) d 2 (d(t)(300ft +10 ft /sec- dt dt dt 2d (t)d'(t) 0+10 ft / secx 2t 10 ft/secxt d'(t) -(1) d(t)

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