Answer:
the net force applied to the car is zero.
Explanation:
According to Newton's second law, the acceleration of an object (a) is directly proportional to the net force applied (F):
![a=\frac{F}{m}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7BF%7D%7Bm%7D)
where m is the object's mass.
In this problem, the car is moving with constant velocity: this means that the acceleration is zero, a = 0. Therefore, according to the previous equation, the net force must also be zero: F = 0. So, the correct answer is
the net force applied to the car is zero.
Answer:
<em>The magnitude of vector d is 16 and the angle with the x-axis is 270°</em>
Explanation:
<u>Operations With Vectors</u>
Given two vectors in rectangular components:
![\vec a=(ax,ay)\ ,\ \vec b=(bx,by)](https://tex.z-dn.net/?f=%5Cvec%20a%3D%28ax%2Cay%29%5C%20%2C%5C%20%20%5Cvec%20b%3D%28bx%2Cby%29)
The sum of the vectors is:
![\vec a+\vec b=(ax+bx,ay+by)](https://tex.z-dn.net/?f=%5Cvec%20a%2B%5Cvec%20b%3D%28ax%2Bbx%2Cay%2Bby%29)
The difference between the vectors is:
![\vec a-\vec b=(ax-bx,ay-by)](https://tex.z-dn.net/?f=%5Cvec%20a-%5Cvec%20b%3D%28ax-bx%2Cay-by%29)
The magnitude of
is:
![|\vec a|=\sqrt{ax^2+ay^2}](https://tex.z-dn.net/?f=%7C%5Cvec%20a%7C%3D%5Csqrt%7Bax%5E2%2Bay%5E2%7D)
The angle
makes with the horizontal positive direction is:
![\displaystyle \tan\theta=\frac{ay}{ax}\\](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctan%5Ctheta%3D%5Cfrac%7Bay%7D%7Bax%7D%5C%5C)
The question provides the vectors:
![\vec a=(2,6)](https://tex.z-dn.net/?f=%5Cvec%20a%3D%282%2C6%29)
![\vec b=(2,22)](https://tex.z-dn.net/?f=%5Cvec%20b%3D%282%2C22%29)
![\vec d=\vec a-\vec b](https://tex.z-dn.net/?f=%5Cvec%20d%3D%5Cvec%20a-%5Cvec%20b)
Calculate:
![\vec d=(2,6)-(2,22)=(0,-16)](https://tex.z-dn.net/?f=%5Cvec%20d%3D%282%2C6%29-%282%2C22%29%3D%280%2C-16%29)
The magnitude of
is:
![|\vec d|=\sqrt{0^2+(-16)^2}=\sqrt{0+256}=16](https://tex.z-dn.net/?f=%7C%5Cvec%20d%7C%3D%5Csqrt%7B0%5E2%2B%28-16%29%5E2%7D%3D%5Csqrt%7B0%2B256%7D%3D16)
The angle is calculated by:
![\displaystyle \tan\theta=\frac{-16}{0}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctan%5Ctheta%3D%5Cfrac%7B-16%7D%7B0%7D)
The division cannot be calculated because the denominator is zero. We need to estimate the correct angle by looking at the components of the vector. Since the x-coordinate is zero and the y-coordinate is negative, the vector points downwards (south), thus the angle must be -90° or 270° if the range goes from 0° to 360°.
The magnitude of vector d is 16 and the angle with the x-axis is 270°
Explanation:
The given data is as follows.
Velocity of bullet,
= 814.8 m/s
Observer distance from marksman, d = 24.7 m
Let us assume that time necessary for report of rifle to reach the observer is t and will be calculated as follows.
t =
(velocity in air = 343 m/s)
= 0.072 sec
Now, before the observer hears the report the distance traveled by the bullet is as follows.
![d_{b} = c_{b} \times t](https://tex.z-dn.net/?f=d_%7Bb%7D%20%3D%20c_%7Bb%7D%20%5Ctimes%20t)
= ![814.8 \times 0.072](https://tex.z-dn.net/?f=814.8%20%5Ctimes%200.072)
= 58.66
= 59 (approx)
Thus, we can conclude that each bullet will travel a distance of 59 m.
The global warming is the uniform heating of the globe due to the effect of greenhouse gases.
Answer: Option B
<u>Explanation:</u>
Global warming is thus the theory that says that earth is warming up with an increase in temperature over time due to increment in the greenhouse gases.
These are greenhouse gases that are getting increased due to the human activity or say over exploitation of the natural resources. The heating of the globe has caused ozone layer depletion which is also causing warming.