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LiRa [457]
3 years ago
14

A watermelon is blown into three pieces by a large firecracker. Two pieces of equal mass m fly away perpendicular to one another

, one in the x direction another in the y direction. Both of these pieces fly away with a speed of V = 42 m/s. The third piece has three times the mass of the other two pieces. Randomized Variables V = 42 m/s show answer No Attempt 33% Part (a) Write an expression for the speed of the larger piece, that is in terms of only the variable V.
Physics
1 answer:
Alenkinab [10]3 years ago
3 0

Answer:

Speed of larger piece is \dfrac{V\sqrt{2}}{3}

Explanation:

We apply the principle of conservation of momentum.

The watermelon is initially at rest. The initial momentum = 0 kg m/s in all directions.

After the collision,

Vertical momentum = momentum of piece in y-direction + y-component of momentum of larger piece = mV + 3mv_{ly}

Here, v_{ly} is the y-component of velocity of larger piece.

This is equal to 0, since the initial momentum is 0.

v_{ly}=\dfrac{V}{3}

Horizontal momentum = momentum of piece in x-direction + x-component of momentum of larger piece = mV + 3mv_{lx}

Here, v_{lx} is the x-component of velocity of larger piece.

This is also equal to 0, since the initial momentum is 0.

v_{lx}=\dfrac{V}{3}

The velocity of the larger piece, v_l, is the resultant of v_{lx} and v_{ly}. Since they are mutually perpendicular,

v_l = \sqrt{v_{ly}^2+v_{lx}^2}= \sqrt{\left(\dfrac{V}{3}\right)^2+\left(\dfrac{V}{3}\right)^2}

v_l = \dfrac{V\sqrt{2}}{3}

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To generate clean energy the mayor my build the fooling type of energy plants:

wind farms

solar power plants

wave power plants

Explanation:

At the seaside there are winds all over the year and that can be transformed in electrical energy by a wind turbine. The mayor can build a on-shore wind farm (reduced consts) and may also build off-shore wind farms (but these have an increased cost).

The second option is to build solar power plants. It will be cost effective if the people in the town will install solar panels on the building roofs. In this way you decrease the costs with the transportation of electrical energy.

The third option is to install wave power plants which harvest energy from the sea waves. It is a rather new technology, in comparison with the other two, but the initial consts can be amortized over time.

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Right now nuclear plants have a very expensive initial costs and they may not be afforded by small towns.

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7 0
3 years ago
A coyote can locate a sound source with good accuracy by comparing the arrival times of a sound wave at its two ears. Suppose a
jeka94

Answer:

a)  t_l - t_r = 12.54 us

b)  (t_l - t_r) / T = 0.0157  

Explanation:

Given:

- Frequency of source f = 1250 Hz

- Distance from source to right ear d_r = 2.6 m

- Distance from source to left ear d_l = ?

- Separation between ears s = 0.15 m

Find:

a. What is the difference in the arrival time of the sound at the left ear and the right ear?

b. What is the ratio of this time difference to the period of the sound wave?

Solution:

- Apply Pythagoras theorem to calculate the distance d_l from source to left ear:

                                      d_l = sqrt ( 2.6^2 + 0.15^2)

                                      d_l = sqrt ( 6.7825 )

                                      d_l = 2.6043 m

- The time deference can be calculated from a simple distance - speed formula:

                                      t_l - t_r = (1 / v) * ( d_l - d_r)

Where, v = 343 m/s speed of sound in air:

                                      t_l - t_r = (1 / 343) * ( 2.6043 - 2.6)  

                                      t_l - t_r = ( 0.0043 / 343 )

                                      t_l - t_r = 12.54 us

- Now we compute the Time period of the sound wave:

                                      T = 1 / f

                                      T = 1 / 1250 = 8*10^-4 s

- The ratio of differential time to Time period T is:

                                      (t_l - t_r) / T = 12.54 * 10^-6 / 8*10^-4

                                      (t_l - t_r) / T = 0.0157  

3 0
3 years ago
Suppose your salary in 2012 is $70,000. Assuming an annual inflation rate of 7%, what salary do you need to earn in 2020 in orde
s2008m [1.1K]

Annual salary(2012) = $70,000

Annual inflation = 7%

Therefore, the salary you need to earn in 2020 in order to have the same purchasing power can be calculated below

2020-2012=8\text{ years}FV=PV\times(1+r)^n

where

n = 8

r = 7/100 = 0.07

PV = 70, 000

\begin{gathered} FV=70,000(1+0.07)^8 \\ FV=70000(1.07)^8 \\ FV\text{ = 70000}\times1.71818617983 \\ FV=120273.032588 \\ FV=\text{  \$}120,273.03 \end{gathered}

The salary you need to earn in 2020 to have the same purchasing power = $120, 273.03

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The new gravitational attraction will be 1/4 as much

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where

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m1, m2 are the masses of the two objects

r is the separation between them

In this problem, the original force between the two objects is F, when they are separated by a distance r.

Later, the distance between the two objects is doubled, so the new distance is

r'=2r

Therefore, the new force will be

F'=G\frac{m_1 m_2}{(2r)^2}=\frac{1}{4}(\frac{Gm_1 m_2}{r^2})=\frac{F}{4}

Therefore, the new force will be one-fourth as much.

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