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4 years ago

5. Find the volume of the composite space figure to the nearest whole number.

1 answer:

6 0

The shape is missing but let's consider it a semi-cylinder attached to the rectangular prism.
Given:
radius = 4.5 mm
Height = 11 mm 

Volume of cylinder = (1/2)(pi)(4.5)^2(11) (the shape is divided into half)
V = 349.89 mm cubed
Volume of prism = L x W x H
= 9 x 11 x 6
= 594 mm cubed
Total volume of the composite shape = 111.375 + 594
= 943.89 mm cubed
Rounded answer = 944 mm cubed.

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3 years ago

A stunt driver wants to make his car jump over 8 cars parked side by side below a horizontal ramp.

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Answer:

a) Minimum speed must he drive off the horizontal ramp = 39.78 m/s

b) Minimum speed must he drive off the horizontal ramp with 7° above the horizontal = 23.93 m/s

Explanation:

a) The height of ramp = 1.5 meter

Horizontal distance he must clear = 22 meter

The car is having horizontal motion and vertical motion. In case of vertical motion the acceleration on the car is acceleration due to gravity.

We have equation of motion, $s= ut+\frac{1}{2} at^2$ , s is the displacement, u is the initial velocity, a is the acceleration and t is the time.

In case of vertical motion initial velocity = 0 m/s, acceleration = 9.8 $m/s^2$ , we need to calculate time when displacement = 1.5 meter.

$1.5=0*t+\frac{1}{2} *9.8*t^2\\ \\ t = 0.553 seconds$

So the car has to cover a distance of 22 meter in 2.119 seconds.

So minimum speed required = 22/0.553 = 39.78 m/s

Minimum speed must he drive off the horizontal ramp = 39.78 m/s

b) When the take of angle is 7⁰ the vertical speed of car is not zero = V sin 7 = 0.122 V

So the in case of vertical motion we have initial velocity = 0.122 V, S = -1.5 meter( below ramp), acceleration = -9.8 $m/s^2$

Substituting

$-1.5=0.122V*t-\frac{1}{2} *9.8*t^2\\ \\ 4.9t^2-0.122Vt-1.5=0$

In case of horizontal motion

Horizontal speed of car = V cos 7 = 0.993V

So it has to travel 22 meter in t seconds

0.993Vt = 22, Vt = 22.155 m

Substituting in the equation $4.9t^2-0.122Vt-1.5=0$

We will get $4.9t^2-0.122*22.155-1.5=0\\ \\ t = 0.926 seconds$

Speed required = 22.155/0.926 = 23.93 m/s

Minimum speed must he drive off the horizontal ramp with 7° above the horizontal = 23.93 m/s

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3 years ago

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3 years ago

Infrared radiation from young stars can pass through the heavy dust clouds surrounding them, allowing astronomers here on Earth

liberstina [14]

Answer:

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Explanation:

The relationship between the wavelength and the frequency of a wave is given by the following equation:

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f = frequency of infrared radiation = 1.61 THz = 1.61 x 10¹² Hz

Therefore,

$\lambda = \frac{3\ x\ 10^8\ m/s}{1.61\ x\ 10^{12}\ Hz}$

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