Answer:
31.75 m/s
Explanation:
h = 41.7 m
Let the initial velocity of the second stone is u
Let the time taken to reach to the bottom by the first stone is t then the time taken by the second stone to reach the ground is t - 1.8.
For first stone:
Use second equation of motion
![h=ut+\frac{1}{2}gt^2](https://tex.z-dn.net/?f=h%3Dut%2B%5Cfrac%7B1%7D%7B2%7Dgt%5E2)
Here, u = 0, g = 9.8 m/s^2 and t be the time and h = 41.7
So, 41.7= 0 + 0.5 x 9.8 x t^2
41.7 = 4.9 t^2
t = 2.92 s ..... (1)
For second stone:
Use second equation of motion
![h=ut+\frac{1}{2}gt^2](https://tex.z-dn.net/?f=h%3Dut%2B%5Cfrac%7B1%7D%7B2%7Dgt%5E2)
Here, g = 9.8 m/s^2 and time taken is t - 1.8 = 2.92 - 1.8 = 1.12 s, h = 41.7 m and u be the initial velocity
.... (2)
By equation the equation (1) and (2), we get
![41.7=1.12 u +4.9 \times 1.12^{2}](https://tex.z-dn.net/?f=41.7%3D1.12%20u%20%2B4.9%20%5Ctimes%201.12%5E%7B2%7D)
u = 31.75 m/s
<span>Anger is to angry as fire is to blazing. </span>
Answer:
The curl is ![0 \hat x -z^2 \hat y -4xy \hat z](https://tex.z-dn.net/?f=0%20%5Chat%20x%20-z%5E2%20%5Chat%20y%20-4xy%20%5Chat%20z)
Explanation:
Given the vector function
![\vec A (\vec r) =4x^3 \hat{x}-2x^2y \hat y+xz^2 \hat z](https://tex.z-dn.net/?f=%5Cvec%20A%20%28%5Cvec%20r%29%20%3D4x%5E3%20%5Chat%7Bx%7D-2x%5E2y%20%5Chat%20y%2Bxz%5E2%20%5Chat%20z)
We can calculate the curl using the definition
![\nabla \times \vec A (\vec r ) = \left|\begin{array}{ccc}\hat x&\hat y&\hat z\\\partial/\partial x&\partial/\partial y&\partial/\partial z\\A_x&X_y&A_z\end{array}\right|](https://tex.z-dn.net/?f=%5Cnabla%20%5Ctimes%20%5Cvec%20A%20%28%5Cvec%20r%20%29%20%3D%20%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D%5Chat%20x%26%5Chat%20y%26%5Chat%20z%5C%5C%5Cpartial%2F%5Cpartial%20x%26%5Cpartial%2F%5Cpartial%20y%26%5Cpartial%2F%5Cpartial%20z%5C%5CA_x%26X_y%26A_z%5Cend%7Barray%7D%5Cright%7C)
Thus for the exercise we will have
![\nabla \times \vec A (\vec r ) = \left|\begin{array}{ccc}\hat x&\hat y&\hat z\\\partial/\partial x&\partial/\partial y&\partial/\partial z\\4x^3&-2x^2y&xz^2\end{array}\right|](https://tex.z-dn.net/?f=%5Cnabla%20%5Ctimes%20%5Cvec%20A%20%28%5Cvec%20r%20%29%20%3D%20%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D%5Chat%20x%26%5Chat%20y%26%5Chat%20z%5C%5C%5Cpartial%2F%5Cpartial%20x%26%5Cpartial%2F%5Cpartial%20y%26%5Cpartial%2F%5Cpartial%20z%5C%5C4x%5E3%26-2x%5E2y%26xz%5E2%5Cend%7Barray%7D%5Cright%7C)
So we will get
![\nabla \times \vec A (\vec r )= \left( \cfrac{\partial}{\partial y}(xz^2)-\cfrac{\partial}{\partial z}(-2x^2y)\right) \hat x - \left(\cfrac{\partial}{\partial x}(xz^2)-\cfrac{\partial}{\partial z}(4x^3) \right) \hat y + \left(\cfrac{\partial}{\partial x}(-2x^2y)-\cfrac{\partial}{\partial y}(4x^3) \right) \hat z](https://tex.z-dn.net/?f=%5Cnabla%20%20%5Ctimes%20%5Cvec%20A%20%28%5Cvec%20r%20%29%3D%20%5Cleft%28%20%5Ccfrac%7B%5Cpartial%7D%7B%5Cpartial%20y%7D%28xz%5E2%29-%5Ccfrac%7B%5Cpartial%7D%7B%5Cpartial%20z%7D%28-2x%5E2y%29%5Cright%29%20%5Chat%20x%20-%20%5Cleft%28%5Ccfrac%7B%5Cpartial%7D%7B%5Cpartial%20x%7D%28xz%5E2%29-%5Ccfrac%7B%5Cpartial%7D%7B%5Cpartial%20z%7D%284x%5E3%29%20%5Cright%29%20%5Chat%20y%20%2B%20%5Cleft%28%5Ccfrac%7B%5Cpartial%7D%7B%5Cpartial%20x%7D%28-2x%5E2y%29-%5Ccfrac%7B%5Cpartial%7D%7B%5Cpartial%20y%7D%284x%5E3%29%20%5Cright%29%20%5Chat%20z)
Working with the partial derivatives we get the curl
![\nabla \times \vec A (\vec r )=0 \hat x -z^2 \hat y -4xy \hat z](https://tex.z-dn.net/?f=%5Cnabla%20%20%5Ctimes%20%5Cvec%20A%20%28%5Cvec%20r%20%29%3D0%20%5Chat%20x%20-z%5E2%20%5Chat%20y%20-4xy%20%5Chat%20z)
Answer:
= 33.33 cm
Explanation:
Given:
When mass,
=21 kg
distance travelled is
= 140 cm
When mass,
=5 kg
distance travelled is
= ?
Hooke's law state that within elastic limit, when an external force is applied to a body, the body gets deformed and when the force is released the gets back to its original form.
Therefore according to the question,
![\frac{d_{1}}{m_{1}}=\frac{d_{2}}{m_{2}}](https://tex.z-dn.net/?f=%5Cfrac%7Bd_%7B1%7D%7D%7Bm_%7B1%7D%7D%3D%5Cfrac%7Bd_%7B2%7D%7D%7Bm_%7B2%7D%7D)
![\frac{140}{21}=\frac{d_{2}}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B140%7D%7B21%7D%3D%5Cfrac%7Bd_%7B2%7D%7D%7B5%7D)
= 33.33 cm
Distance travelled is 33.33 cm when mass is 5 kg.