First method
initial distance = 16m
final distance= 43 m
total distance covered= final -initial
=43m -16m
=27m
Second method
Si= 16m
Sf =43 m
t= 12 s
first we will find V
V = (Sf-Si)/ t
V =( 43- 16)/ 12
V = 27/12 ⇒ V= 9/4
V= distance / time
distance= V×time
distance = (9/4) ×12
distance =27
B. Both of these types of lenses have the ability to produce real images.
Answer:
The angular momentum of the particle is 58.14 kg m²/s along positive z- axis and is independent of time .
Explanation:
Given that,
Mass = 1.70 kg
Position vector ![r=(6.00\hat{i}+5.70 t \hat{j})](https://tex.z-dn.net/?f=r%3D%286.00%5Chat%7Bi%7D%2B5.70%20t%20%5Chat%7Bj%7D%29)
We need to calculate the angular velocity
The velocity is the rate of change of the position of the particle.
![v = \dfrac{dr}{dt}](https://tex.z-dn.net/?f=v%20%3D%20%5Cdfrac%7Bdr%7D%7Bdt%7D)
![v=\dfrac{d}{dt}(6.00\hat{i}+5.70 t \hat{j})](https://tex.z-dn.net/?f=v%3D%5Cdfrac%7Bd%7D%7Bdt%7D%286.00%5Chat%7Bi%7D%2B5.70%20t%20%5Chat%7Bj%7D%29)
![v=5.70\hat{j}](https://tex.z-dn.net/?f=v%3D5.70%5Chat%7Bj%7D)
We need to calculate the angular momentum of the particle
Using formula of angular momentum
![L=r\cdot p](https://tex.z-dn.net/?f=L%3Dr%5Ccdot%20p)
Where, p = mv
Put the value of p into the formula
![L=m(r\times v)](https://tex.z-dn.net/?f=L%3Dm%28r%5Ctimes%20v%29)
Substitute the value into the formula
![L=1.70(6.00\hat{i}+5.70 t \hat{j}\times5.70\hat{j})](https://tex.z-dn.net/?f=L%3D1.70%286.00%5Chat%7Bi%7D%2B5.70%20t%20%5Chat%7Bj%7D%5Ctimes5.70%5Chat%7Bj%7D%29)
![L=1.70\times34.2](https://tex.z-dn.net/?f=L%3D1.70%5Ctimes34.2)
![L=58.14\ kgm^2/s](https://tex.z-dn.net/?f=L%3D58.14%5C%20kgm%5E2%2Fs)
Hence, The angular momentum of the particle is 58.14 kg m²/s along positive z- axis and is independent of time .
Answer:
Explanation:
<u>Kinematics equation for first Object:</u>
![y(t)=y_{o}+v_{o}t-1/2*g*t^{2}](https://tex.z-dn.net/?f=y%28t%29%3Dy_%7Bo%7D%2Bv_%7Bo%7Dt-1%2F2%2Ag%2At%5E%7B2%7D)
but:
The initial velocity is zero
![y_{o}=20m](https://tex.z-dn.net/?f=y_%7Bo%7D%3D20m)
it reach the water at in instant, t1, y(t)=0:
![0=y_{o}-1/2*g*t_{1}^{2}](https://tex.z-dn.net/?f=0%3Dy_%7Bo%7D-1%2F2%2Ag%2At_%7B1%7D%5E%7B2%7D)
![t_{1}=\sqrt{2y_{o}/g}=\sqrt{2*20/9.81}=2.02s](https://tex.z-dn.net/?f=t_%7B1%7D%3D%5Csqrt%7B2y_%7Bo%7D%2Fg%7D%3D%5Csqrt%7B2%2A20%2F9.81%7D%3D2.02s)
<u>Kinematics equation for the second Object:</u>
The initial velocity is zero
![y(t)=y_{o}+v_{o}t-1/2*g*t^{2}](https://tex.z-dn.net/?f=y%28t%29%3Dy_%7Bo%7D%2Bv_%7Bo%7Dt-1%2F2%2Ag%2At%5E%7B2%7D)
but:
![y_{o}=20m](https://tex.z-dn.net/?f=y_%7Bo%7D%3D20m)
it reach the water at in instant, t2, y(t)=0. If the second object is thrown 1s later, t2=t1-1=1.02s
![0=y_{o}+v_{o}t_{2}-1/2*g*t_{2}^{2}](https://tex.z-dn.net/?f=0%3Dy_%7Bo%7D%2Bv_%7Bo%7Dt_%7B2%7D-1%2F2%2Ag%2At_%7B2%7D%5E%7B2%7D)
The velocity is negative, because the object is thrown downwards.