Jamie begins her journey at 15 km and ends her journey at 75 km. She travels for a total of 3 h. What is her velocity?

A 0.29 kg particle moves in an xy plane according to x(t) = - 19 + 1 t - 3 t3 and y(t) = 20 + 7 t - 9 t2, with x and y in meters

Artist 52 [7]

Answer:

Part a)

$F = 7.76 N$

Part b)

$\theta = -137.7 degree$

Part c)

$\theta = -127.7 degree$

Explanation:

As we know that acceleration is rate of change in velocity of the object

So here we know that

$x = -19 + t - 3t^3$

$y = 20 + 7t - 9t^2$

Part a)

differentiate x and y two times with respect to time to find the acceleration

$a_x = \frac{d^2}{dt^2}(-19 + t - 3t^3)$

$a_x = \frac{d}{dt}(0 +1 - 9t^2)$

$a_x = -18t$

$a_y = \frac{d^2}{dt^2}(20 + 7t - 9t^2)$

$a_y = \frac{d}{dt}(0 +7 - 18t)$

$a_y = -18$

Now the acceleration of the object is given as

$\vec a = (-18t)\hat i + (-18)\hat j$

at t= 1.1 s we have

$\vec a = -19.8 \hat i - 18 \hat j$

now the net force of the object is given as

$\vec F = m\vec a$

$\vec F = (0.29 kg)(-19.8 \hat i - 18 \hat j)$

$\vec F = -5.74 \hat i - 5.22 \hat j$

now magnitude of the force will be

$F = \sqrt{5.74^2 + 5.22^2} = 7.76 N$

Part b)

Direction of the force is given as

$tan\theta = \frac{F_y}{F_x}$

$tan\theta = \frac{-5.22}{-5.74}$

$\theta = -137.7 degree$

Part c)

For velocity of the particle we have

$v_x = \frac{dx}[dt}$

$v_x = (0 +1 - 9t^2)$

$v_y = \frac{dy}{dt}$

$v_y = (0 +7 - 18t)$

now at t = 1.1 s

$\vec v = -9.89\hat i - 12.8 \hat j$

now the direction of the velocity is given as

$\theta = tan^{-1}(\frac{v_y}{v_x})$

$\theta = tan^{-1}(\frac{-12.8}{-9.89})$

$\theta = -127.7 degree$

7 0

3 years ago

You throw a rock horizontally out of a 7th story window. You time that it takes 3.7 seconds to hit the ground, and measure that

Nady [450]

Since we are only looking at the vertical height, we can use the free fall equation to find the height:
h = 0.5*g*t^2, where h is height in m, g is acceleration due to gravity (9.81 m/s^2), and t is time in seconds
h = 0.5*(9.81 m/s^2)*(3.7 s)^2
h = 67.15 m
Therefore, the 7th floor window is 67.15 m above ground level.

5 0

3 years ago

Which is more reliable—using a manual stop watch or using light gates?<br> Explain.

Kitty [74]

Light gates are more reliable. When using a manual stop watch, it is difficult to stop it at an exact time. A light gate is able to detect when an object passes through a 'gate' with the infrared transmitter and receiver.

7 0

4 years ago

Why is it important to develop alternative energy sources

Aliun [14]

Answer:

The alternative energy sources are defined as those resources that are used in place of the natural and non-renewable resources. This resources plays an important role in the conservation of natural resources.

The fossil fuels are the resources on which the people are directly dependent. Burning up of these fossils leads to the emission of carbon, which has a direct impact on earth. A small increase in the amount of carbon dioxide can lead to the increase in the surface temperature of earth.

In addition to this, these fossil fuels such as coal, petroleum, oil and natural gases are found to be present in a limited proportion, and it is a very expensive process to obtain these resources, so sustainable development method must be adopted in order to save this natural resources for the future generation.

Some of the examples of alternative resources that are widely used in place of fossil fuels are wind energy, solar energy, tidal energy, biomass energy and bio-fuels.

Thus, it is very important to develop and use alternative resources.

7 0

3 years ago

Balboa Park in San Diego has an outdoor organ. When the air temperature increases, the fundamental frequency of one of the organ

musickatia [10]

The fundamental frequency of one of the organ pipes will go up or increase.

When pressured air is forced into an organ pipe, it echoes at a particular pitch, generating the sound of the pipe organ. Each pipe has been adjusted to a particular pitch on the musical scale.

A musical instrument called an outdoor pipe organ is used to perform music. It produces some calming tones and has a really serene sound. The organ pipe produces the sound of the outdoor organ. The wavelength of the sound is also dependent on the length of the pipe. The fundamental frequency of one of the organ pipes will grow as the speed of the sound increases as the ambient air temperature rises.

The correct option is (c).

Learn more about frequency here:

brainly.com/question/254161

#SPJ4

6 0

1 year ago