Answer:
1)
2)
3)
Explanation:
Given:
width of river,
speed of stream with respect to the ground,
speed of the swimmer with respect to water,
<u>Now the resultant of the two velocities perpendicular to each other:</u>
<u>Now the angle of the resultant velocity form the vertical:</u>
- Now the distance swam by the swimmer in this direction be d.
so,
Now the distance swept downward:
2)
On swimming 37° upstream:
<u>The velocity component of stream cancelled by the swimmer:</u>
<u>Now the net effective speed of stream sweeping the swimmer:</u>
<u>The component of swimmer's velocity heading directly towards the opposite bank:</u>
<u>Now the angle of the resultant velocity of the swimmer from the normal to the stream</u>:
- Now let the distance swam in this direction be d'.
<u>Now the distance swept downstream:</u>
3)
Time taken in crossing the rive in case 1:
Time taken in crossing the rive in case 2:
Answer:
0.471Nm downwards.
Explanation:
For this problem we need to apply the Torque equation,
That is
Where N is the number of turns, A is the area, B is magnetic field and \theta is the angle loop mae with B
We calculate the area, so
Replacing in the equation of Torque,
We can conclude that the magnutide of maximum torque is 0.471Nm downwards.
Answer:
Explanation:
It is given that,
Charge at origin,
Let second charge is and it is placed at x = 0.1 m
Resulting force on the second charge,
The electric force acting on the charged particles is given by the following formula as :
So, the second charge is . Hence, this is the required solution.
Answer:
Explanation:
stiffness k = 160
m = 10
angular frequency ω =
=
= 4
ω = 4
Let x = 4 - A sinωt
when t = 0
x = 4 in
when t = 2 s , x = - 4
- 4 = 4 - A sinωt
8 = A sin 4 x 2
8 = A sin8
A = 8 / sin 8
= 8 / .989
= 8.09 in .
x = 4 - A sinωt
dx / dt = - Aω cosωt
v = - Aω cosωt
for t = 0
v = - Aω
= - 8.09 x 4
= - 32.36 in / s
initial velocity v = - 32.36 in /s
displacement x for t = 4s
x = 4 - 8.09 sin 4 x 4
= 4 - 8.09 sin 16
= 4 - 8.09 x - .2879
= 4 + 2.33
= 6.33 in.
c ) Amplitude of vibration A = 8.09 in .as calculated above .