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zheka24 [161]
3 years ago
13

A small balloon is released at a point 150 feet away from an observer, who is on level ground. If the balloon goes straight up a

t a rate of 7 feet per second, how fast is the distance from the observer to the balloon increasing when the balloon is 14 feet high

Physics
1 answer:
Elza [17]3 years ago
5 0

Answer:

\dfrac{dz}{dt}=0.65\ ft/s

Explanation:

Given that

x= 150 ft

\dfrac{dy}{dt}= 7\ ft/s

y= 14 ft

From the diagram

z^2=x^2+y^2

When ,x= 150 ft and y= 14 ft

z^2=150^2+14^2

z=\sqrt{150^2+15^2}

z=150.74 ft

z^2=x^2+y^2

By differentiating with respect to time t

2z\dfrac{dz}{dt}= 2x\dfrac{dx}{dt}+2y\dfrac{dy}{dt}

z\dfrac{dz}{dt}= x\dfrac{dx}{dt}+y\dfrac{dy}{dt}

Here x is constant that is why

\dfrac{dx}{dt}=0

z\dfrac{dz}{dt}= y\dfrac{dy}{dt}

Now by putting the values in the above equation we get

150.74\times \dfrac{dz}{dt}=14\times 7

\dfrac{dz}{dt}=\dfrac{14\times 7}{150.74}\ ft/s

\dfrac{dz}{dt}=0.65\ ft/s

Therefore the distance between balloon and observer increasing with 0.65 ft/s.

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The vertical position at time t is given by

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where

h = 2.5 km = 2500 m is the initial height

u_y = 0 is the initial vertical velocity of the cargo

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The cargo reaches the ground when

y(t) = 0

So substituting it into the equation and solving for t, we find the time of flight of the cargo:

0 = h - \frac{1}{2}gt^2\\t=\sqrt{\frac{2h}{g}}=\sqrt{\frac{2(2500)}{9.8}}=22.6 s

b) 7.5 km

The range travelled by the cargo can be calculated by considering its horizontal motion only. In fact, the horizontal motion is a uniform motion, with constant velocity equal to the initial velocity of the jet:

v_x = 1200 km/h \cdot \frac{1000 m/km}{3600 s/h}=333.3 m/s

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d=(333.3)(22.6)=7533 m = 7.5 km

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Answer:

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Explanation:

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In this problem, we have

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Explanation:

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Human beings discovered that down feathers are good for insulation long ago. For example, documents from the 1600s show that Russian merchants sold “bird down" to the Dutch hundreds of years ago.

Today, down is used in all sorts of products, including coats, bedding, and sleeping bags, to help better insulate the user from cold weather. Down can be collected from many different types of birds, but most of today's supply comes from domestic geese.

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13.875 T

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Current, I = 1.85 A

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