Answer:
c. initial (x and y)
Explanation:
When a projectile is launched at a velocity with a launch angle, to solve it, we must first resolve the initial velocity into the x and y components. To do this will mean we have to treat it like a triangle due to the launch angle and the direction of the projectile.
Therefore, we will have to make use of trigonometric ratios which is also known by the mnemonic "SOH CAH TOA"
Thus, this method resolves the initial x and y velocities.
Answer:
M
Explanation:
To apply the concept of <u>angular momentum conservation</u>, there should be no external torque before and after
As the <u>asteroid is travelling directly towards the center of the Earth</u>, after impact ,it <u>does not impose any torque on earth's rotation,</u> So angular momentum of earth is conserved
⇒![I_{1} \times W_{1} =I_{2} \times W_{2}](https://tex.z-dn.net/?f=I_%7B1%7D%20%5Ctimes%20W_%7B1%7D%20%3DI_%7B2%7D%20%5Ctimes%20W_%7B2%7D)
-
is the moment of interia of earth before impact -
is the angular velocity of earth about an axis passing through the center of earth before impact
is moment of interia of earth and asteroid system
is the angular velocity of earth and asteroid system about the same axis
let ![W_{1}=W](https://tex.z-dn.net/?f=W_%7B1%7D%3DW)
since ![\text{Time period of rotation}∝](https://tex.z-dn.net/?f=%5Ctext%7BTime%20period%20of%20rotation%7D%E2%88%9D)
![\frac{1}{\text{Angular velocity}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Ctext%7BAngular%20velocity%7D%7D)
⇒ if time period is to increase by 25%, which is
times, the angular velocity decreases 25% which is
times
therefore
![\frac{4}{5} \times W_{1}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B5%7D%20%5Ctimes%20W_%7B1%7D)
(moment of inertia of solid sphere)
where M is mass of earth
R is radius of earth
![I_{2}=\frac{2}{5} \times M\times R^{2}+M_{1}\times R^{2}](https://tex.z-dn.net/?f=I_%7B2%7D%3D%5Cfrac%7B2%7D%7B5%7D%20%5Ctimes%20M%5Ctimes%20R%5E%7B2%7D%2BM_%7B1%7D%5Ctimes%20R%5E%7B2%7D)
(As given asteroid is very small compared to earth, we assume it be a particle compared to earth, therefore by parallel axis theorem we find its moment of inertia with respect to axis)
where
is mass of asteroid
⇒ ![\frac{2}{5} \times M\times R^{2} \times W_{1}=}(\frac{2}{5} \times M\times R^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B5%7D%20%5Ctimes%20M%5Ctimes%20R%5E%7B2%7D%20%5Ctimes%20W_%7B1%7D%3D%7D%28%5Cfrac%7B2%7D%7B5%7D%20%5Ctimes%20M%5Ctimes%20R%5E%7B2%7D)
![M_{1}\times R^{2})\times(\frac{4}{5} \times W_{1})](https://tex.z-dn.net/?f=M_%7B1%7D%5Ctimes%20R%5E%7B2%7D%29%5Ctimes%28%5Cfrac%7B4%7D%7B5%7D%20%5Ctimes%20W_%7B1%7D%29)
=
+ ![M_{1}\times R^{2})](https://tex.z-dn.net/?f=M_%7B1%7D%5Ctimes%20R%5E%7B2%7D%29)
![\frac{1}{10} \times M\times R^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B10%7D%20%5Ctimes%20M%5Ctimes%20R%5E%7B2%7D)
⇒![M_{1}=}](https://tex.z-dn.net/?f=M_%7B1%7D%3D%7D)
![\frac{1}{10} \times M](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B10%7D%20%5Ctimes%20M)
They almost entirely reside within galaxies because quasars are a subset of blackholes with a large and fast enough accretion disk to generate a beam of interstellar material perpendicular to itself. This typically only occurs in the largest black holes at the center of galaxies (supermassive blackholes) or at least stellar black holes---which still occur within galaxies because the material is necessary to form them.
Answer:
![\boxed {\boxed {\sf 4.5 \ m/s \ in \ the \ positive \ direction}}](https://tex.z-dn.net/?f=%5Cboxed%20%7B%5Cboxed%20%7B%5Csf%204.5%20%5C%20m%2Fs%20%5C%20in%20%5C%20the%20%20%5C%20positive%20%5C%20direction%7D%7D)
Explanation:
We are asked to find the final velocity of the boat.
We are given the initial velocity, acceleration, and time. Therefore, we will use the following kinematic equation.
![v_f= v_i + at](https://tex.z-dn.net/?f=v_f%3D%20v_i%20%2B%20at)
The initial velocity is 2.7 meters per second. The acceleration is 0.15 meters per second squared. The time is 12 seconds.
= 2.7 m/s - a= 0.15 m/s²
- t= 12 s
Substitute the values into the formula.
![v_f = 2.7 \ m/s + (0.15 \ m/s^2)(12 \ s)](https://tex.z-dn.net/?f=v_f%20%3D%202.7%20%5C%20m%2Fs%20%2B%20%280.15%20%5C%20m%2Fs%5E2%29%2812%20%5C%20s%29)
Multiply the numbers in parentheses.
![v_f= 2.7 \ m/s + (0.15 \ m/s/s * 12 \ s)](https://tex.z-dn.net/?f=v_f%3D%202.7%20%5C%20m%2Fs%20%2B%20%280.15%20%5C%20m%2Fs%2Fs%20%2A%2012%20%5C%20s%29)
![v_f = 2.7 \ m/s + (0.15 \ m/s *12)](https://tex.z-dn.net/?f=v_f%20%3D%202.7%20%5C%20m%2Fs%20%2B%20%280.15%20%5C%20m%2Fs%20%2A12%29)
![\v_f=2.7 \ m/s + (1.8 \ m/s)](https://tex.z-dn.net/?f=%5Cv_f%3D2.7%20%5C%20m%2Fs%20%2B%20%281.8%20%5C%20m%2Fs%29)
![v_f=2.7 \ m/s + (1.8 \ m/s)](https://tex.z-dn.net/?f=v_f%3D2.7%20%5C%20m%2Fs%20%2B%20%281.8%20%5C%20m%2Fs%29)
Add.
![v_f=4.5 \ m/s](https://tex.z-dn.net/?f=v_f%3D4.5%20%5C%20m%2Fs)
The final velocity of the boat is <u>4.5 meters per second in the positive direction.</u>