Answer:
D = 43 m
Explanation:
given,
initial velocity = 18 m/s
angle θ = 60°
total horizontal distance covered by the shell is
applying conservation of momentum in horizontal direction
m v₀ cos θ = m₁v₁ + m₂ v₂
m v₀ cos θ = 0.5 m v₂
v₂ = 2 v₀ cos θ.
distance covered by the shell from point of explosion
R' = v t
= 
=
= 
= R
total distance traveled by the shell is
D = 
= 1.5 R
= 
D = 
= 42.9 ≅ 43 m
D = 43 m
Incomplete question. Full text is:
"<span>Give an example of a situation in which you would describe an object's position in (a) one-dimension coordinates (b) two-dimension coordinates (c) three-dimension coordinates"
Solution
(a) One dimension example: a man walking along a metal plank. We just need to specify one coordinate, the distance from the beginning of the plank.
(b) Two-dimension example: a ball moving on a circle. In this case, we need two coordinates: (x,y) to specify the position of the ball at every instant, since it is moving on a 2-D plane.
(c) The position of an airplane in the air: in this case we need 3 coordinates, the height, the latitude and the longitude of the airplane.</span>
Answer:
The observed frequency by the pedestrian is 424 Hz.
Explanation:
Given;
frequency of the source, Fs = 400 Hz
speed of the car as it approaches the stationary observer, Vs = 20 m/s
Based on Doppler effect, as the car the approaches the stationary observer, the observed frequency will be higher than the transmitted (source) frequency because of decrease in distance between the car and the observer.
The observed frequency is calculated as;
![F_s = F_o [\frac{v}{v_s + v} ] \\\\](https://tex.z-dn.net/?f=F_s%20%3D%20F_o%20%5B%5Cfrac%7Bv%7D%7Bv_s%20%2B%20v%7D%20%5D%20%5C%5C%5C%5C)
where;
F₀ is the observed frequency
v is the speed of sound in air = 340 m/s
![F_s = F_o [\frac{v}{v_s + v} ] \\\\400 = F_o [\frac{340}{20 + 340} ] \\\\400 = F_o (0.9444) \\\\F_o = \frac{400}{0.9444} \\\\F_o = 423.55 \ Hz \\](https://tex.z-dn.net/?f=F_s%20%3D%20F_o%20%5B%5Cfrac%7Bv%7D%7Bv_s%20%2B%20v%7D%20%5D%20%5C%5C%5C%5C400%20%3D%20F_o%20%5B%5Cfrac%7B340%7D%7B20%20%2B%20340%7D%20%5D%20%5C%5C%5C%5C400%20%3D%20F_o%20%280.9444%29%20%5C%5C%5C%5CF_o%20%3D%20%5Cfrac%7B400%7D%7B0.9444%7D%20%5C%5C%5C%5CF_o%20%3D%20423.55%20%5C%20Hz%20%5C%5C)
F₀ ≅ 424 Hz.
Therefore, the observed frequency by the pedestrian is 424 Hz.
- The angular acceleration of the wheel approximately <u>-0.76 rad/s² or proportionally as deceleration approximately 0.76 rad/s</u>.
- It need approximately <u>14.474 s</u> to come to rest.
<h2>Introduction</h2>
Hi ! I will help you to discuss about Proportionally Changes in Circular Motion. The analogy of proportionally changes in circular motion is same as the analogy of proportionally changes in direct motion. Here you will hear again the terms acceleration and change in speed, only expressed in the form of a certain angle coverage. Before that, in circular motion, it is necessary to know the following conditions:
- 1 rotation = 2π rad
- 1 rps = 2π rad/s
- 1 rpm =
= 
<h2>Formula Used</h2>
The following equations apply to proportionally changes circular motion:
<h3>Relationship between Angular Acceleration and Change of Angular Velocity </h3>
With the following conditions:
= final angular velocity (rad/s)
= initial angular velocity (rad/s)
= angular acceleration (rad/s²)- t = interval of the time (s)
<h3>Relationship between Angular Acceleration and Change of
(Angle of Rotation) </h3>
Or
With the following condition :
- = change of the sudut (rad)
- = angular acceleration (rad/s²)
- t = interval of the time (s)
- = final angular velocity (rad/s)
- = initial angular velocity (rad/s)
<h2>Problem Solving</h2>
We know that :
- = final angular velocity = 0 rad/s >> see in the sentence "in the process of coming to rest."
- = initial angular velocity = 11 rad/s
- = change of the sudut = 80.0 rad
What was asked :
- = angular acceleration = ... rad/s²
- t = interval of the time = ... s
Step by step :
- = ... rad/s²
<h3>Conclusion</h3>
So :
- The angular acceleration of the wheel approximately -0.76 rad/s² or proportionally as deceleration approximately 0.76 rad/s.
- It need approximately 14.474 s to come to rest.
