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SashulF [63]
3 years ago
14

A hot air balloon is on the ground, 200 feet from an observer. The pilot decides to ascend at 100 ft/min. How fast is the angle

of elevation changing when the balloon is at an altitude of 2500 feet?
Physics
1 answer:
liq [111]3 years ago
6 0

Answer:

0.0031792338 rad/s

Explanation:

\theta = Angle of elevation

y = Height of balloon

Using trigonometry

tan\theta=y\dfrac{y}{200}\\\Rightarrow y=200tan\theta

Differentiating with respect to t we get

\dfrac{dy}{dt}=\dfrac{d}{dt}200tan\theta\\\Rightarrow \dfrac{dy}{dt}=200sec^2\theta\dfrac{d\theta}{dt}\\\Rightarrow 100=200sec^2\theta\dfrac{d\theta}{dt}\\\Rightarrow \dfrac{d\theta}{dt}=\dfrac{100}{200sec^2\theta}\\\Rightarrow \dfrac{d\theta}{dt}=\dfrac{1}{2}cos^2\theta

Now, with the base at 200 ft and height at 2500 ft

The hypotenuse is

h=\sqrt{200^2+2500^2}\\\Rightarrow h=2507.98\ ft

Now y = 2500 ft

cos\theta=\dfrac{200}{h}\\\Rightarrow cos\theta=\dfrac{200}{2507.98}=0.07974

\dfrac{d\theta}{dt}=\dfrac{1}{2}\times 0.07974^2\\\Rightarrow \dfrac{d\theta}{dt}=0.0031792338\ rad/s

The angle is changing at 0.0031792338 rad/s

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A hammer strikes one end of a thick iron rail of length 8.80 m. A microphone located at the opposite end of the rail detects two
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Answer:

ΔT = 0.02412 s

Explanation:

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FOR THE WAVE TRAVELING THROUGH AIR:

T_{air} = \frac{Distance}{Speed\ of\ Sound\ in\ Air}\\\\T_{air} = \frac{8.8\ m}{343\ m/s}\\\\T_{air} = 0.0256\ s

The separation in time between two pulses can now be given as follows:

\Delta T = T_{air}-T_{rail} \\\Delta T = 0.0256\ s - 0.00148\ s\\

<u>ΔT = 0.02412 s</u>

3 0
3 years ago
A soldier throws a grenade horizontally from the top of a cliff. Which of the following curves best describes the path taken by
Natasha_Volkova [10]

Answer:

4. Parabola

Explanation:

The motion of the flight of the grenade is a projectile motion, it's shape is best illustrated using a parabolic diagram.

It's not a circle as the path is not totally round.

It's not an ellipse as the path of motion is not a a completely bounded shape.

Its not a hyperbola as a hyperbola is an open curve with two branches.

Its a parabolic shape because a parabola has just one branch

7 0
3 years ago
2.5 gram sample of a radioactive element was formed in a 1960 explosion of an atomic bomb at Johnson Island in the Pacific Test
kow [346]

Answer:

0.15625 grams

Explanation:

Half life: It is related to the decay of radioactive material. The duration in which  half of the material will be degraded/decayed. That means after half life 50% of the radioactive material will be left. Here the half life is 28 years.

Initial quantity of the sample: 2.5 grams.

After 28 years, the leftover quantity = 1.25 grams

After 56 years, the leftover quantity = 0.625 grams

After 84 Years, the leftover quantity = 0.3125 grams

After 112 years, the leftover quantity = 0.15625 grams

5 0
3 years ago
Explain why the ion formed has a positive charge
AleksAgata [21]
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8 0
3 years ago
Larger animals use proportionately less energy than smaller animals; that is, it takes less energy per kg to power an elephant t
marin [14]

Answer:

Part a)

Q = 952 cal/day

Part b)

P = 46 Watt

Part c)

\Delta P = 54 W

Explanation:

As we know that 5000 kg African elephant requires 70,000 Cal for basic needs per day

so we will have

m = 5000 kg

Q = 70,000 Cal

so we have energy required per kg

E = \frac{70,000}{5000}

E = 14 cal/kg

Part a)

now we know that per kg the energy required will be same

so we have mass of the human is 68 kg

so energy required per day is given as

Q = 68 \times 14

Q = 952 cal/day

Part b)

Resting power is the rate of energy in Joule required per sec

so it is given as

P = \frac{952 \times 4186}{24\times 3600}

P = 46 Watt

Part c)

resting power given in the book is

P' = 100 W

so this is less than the power given

\Delta P = 100 - 46

\Delta P = 54 W

6 0
3 years ago
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