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2 years ago

Ferdinand the frog is hopping from lily pad to lily pad in search of a good fly

Physics

1 answer:

loris [4]2 years ago

4 0

Answer: $36.86\°$

Explanation:

According to the described situation we have the following data:

Horizontal distance between lily pads: $d=2.4 m$

Ferdinand's initial velocity: $V_{o}=5 m/s$

Time it takes a jump: $t=0.6 s$

We need to find the angle $\theta$ at which Ferdinand jumps.

In order to do this, we first have to find the <u>horizontal component (or x-component)</u> of this initial velocity. Since we are dealing with parabolic movement, where velocity has x-component and y-component, and in this case we will choose the x-component to find the angle:

$V_{x}=\frac{d}{t}$ (1)

$V_{x}=\frac{2.4 m}{0.6 s}$ (2)

$V_{x}=4 m/s$ (3)

On the other hand, the x-component of the velocity is expressed as:

$V_{x}=V_{o}cos\theta$ (4)

Substituting (3) in (4):

$4 m/s=5 m/s cos\theta$ (5)

Clearing $\theta$ :

$\theta=cos^{-1} (\frac{4 m/s}{5 m/s})$

$\theta=36.86\°$ This is the angle at which Ferdinand the frog jumps between lily pads

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Complete Question:

The Voyager 1 spacecraft is now beyond the outer reaches of our solar system, but earthbound scientists still receive data from the spacecraft s 20-W radio transmitter. Voyager is expected to continue transmitting until about 2025, when it will be some 25 billion km from Earth.

What s the diameter of a dish antenna that will receive 10−20W of power from Voyager at this time? Assume that the radio transmitter on Voyager transmits equally in all directions(isotropically). In fact, the antenna on Voyager focuses the signal in a beam aimed at the earth, so this problem over-estimates the size of the receiving dish needed.

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d = 2,236 m.

Explanation:

The received power on Earth, can be calculated as the product of the intensity (or power density) times the area that intercepts the power radiated.

As we assume that the transmitter antenna is ominidirectional, power is spreading out over a sphere with a radius equal to the distance to the source.

So, we can get the power density as follows:

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⇒ I = 20 W / 4*π* (25*10¹²)² m²

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Answer:

The total number of small cylinder = 7.

Explanation:

Lets take

Radius of the large cylinder = R

length = L

L = 10 R

The total area A = 2 π R² + π R L

The length of the small cylinder = l

The number of small cylinder = n

L = n l

The total area of small cylinders

A'=n (2 π R² + π R l)

As we know that emissive power given as

P = A ε σ T⁴

For large cylinder

P = A ε σ T⁴ -----------1

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P'=A' ε σ T⁴ ------2

From 1 and 2

Given that

P'= 2 P

A' ε σ T⁴ =2 A ε σ T⁴

A'=2 A (All others are constant)

n (2 π R² + π R l) =(2 2 π R² + π R L)

n (2 R² + R l) = (2 R² + R L)

$n(2R^2+R\times \dfrac{L}{n}) = 2(2R^2+RL)$

L = 10 R

$n(2R^2+R\times \dfrac{10R}{n}) =2 (2R^2+R\times 10R)$

$n(2+\dfrac{10}{n}) =2( 2+ 10)$

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2 n +10 = 24

2 n = 24 -10

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2 years ago