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gayaneshka [121]

3 years ago

8

Suppose that you are headed toward a plateau 55 meters high. If the angle of elevation to the top of the plateau is 40degrees,

how far are you from the base of the plateau?

1 answer:

Iteru [2.4K]3 years ago

3 0

Answer:

$x=65.55m$

Explanation:

Let x be the distance to the shore

From trigonometry properties:

$tan(40^{o} )=\frac{55m}{x} \\x=\frac{55m}{tan(40^{o} )} \\x=65.55m$

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An object thrown in the air has a velocity after t seconds that can be described by v(t) = -9.8t + 24 (in meters/second) and a h

marin [14]

Answer and Explanation: Kinetic energy is related to movement: it is the energy an object possesses during the movement. it is calculated as:

$K=\frac{1}{2}mv^{2}$

For the object thrown in the air:

$K=\frac{1}{2}.2.[v(t)]^{2}$

$K=(-9.8t+24)^{2}$

$K=96.04t^{2}-470.4t+576$

Kinetic energy of the object as a function of time: $K=96.04t^{2}-470.4t+576$

Potential energy is the energy an object possesses due to its position in relation to other objects. It is calculated as:

$U=mgh$

For the object thrown in the air:

$U=9.8.2.h(t)$

$U=9.8.2.(-4.9t^{2}+24t+60)$

$U=-96.04t^{2}+470.4t+1176$

Potential energy as function of time: $U=-96.04t^{2}+470.4t+1176$

Total kinetic and potential energy, also known as mechanical energy is

TME = $96.04t^{2}-470.4t+576$ + ( $-96.04t^{2}+470.4t+1176$ )

TME = 1752

The expression shows that total energy of an object thrown in the air is constant and independent of time.

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A heat pump is to be used for heating a house in winter. The house is to be maintained at 70°F at all times. When the temperatur

Anna35 [415]

Answer:

$\dot{W_{H} } = 4244.48 Btu/h$

Explanation:

Temperature of the house, $T_{H} = 70^{0} F$

Convert to rankine, $T_{H} = 70^{0}+ 460 = 530 R$

Heat is extracted at 40°F i.e $T_{L} = 40^{0}F = 40 + 460 = 500 R$

Calculate the coefficient of performance of the heat pump, COP

$COP = \frac{T_{H} }{T_{H} - T_{L} } \\COP = \frac{530 }{530 - 500 }\\ COP = \frac{530}{30} \\COP = 17.67$

The minimum power required to run the heat pump is given by the formula:

$\dot{W_{H} } = \frac{\dot{Q_{H} }}{COP} \\$ ...............(*)

Where the heat losses from the house, $\dot{Q_{H} } = 75,000 Btu/h$

Substituting these values into * above

$\dot{W_{H} } = \frac{75000}{17.67} \\ \dot{W_{H} } = 4244.48 Btu/h$

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3 years ago