A river 500 ft wide flows with a speed of 8 ft/s with respect to the earth. A woman swims with a speed of 4 ft/s with respect to the water.
1) If the woman heads directly across the river, how far downstream is she swept when she reaches the opposite bank?
2) If she wants to be swept a smaller distance downstream, she heads a bit upstream. Suppose she orients her body in the water at an angle of 37° upstream (where 0° means heading straight accross, how far downstream is she swept before reaching the opposite bank?
3) For the conditions, how long does it take for her to reach the opposite bank?

1)

2)  

3)

Explanation:

Given:

width of river,

speed of stream with respect to the ground,

speed of the swimmer with respect to water,

Now the resultant of the two velocities perpendicular to each other:

Now the angle of the resultant velocity form the vertical:

so,

Now the distance swept downward:

2)

On swimming 37° upstream:

The velocity component of stream cancelled by the swimmer:

Now the net effective speed of stream sweeping the swimmer:

The  component of swimmer's velocity heading directly towards the opposite bank:

Now the angle of the resultant velocity of the swimmer from the normal to the stream:

Now the distance swept downstream:

3)

Time taken in crossing the rive in case 1:

Time taken in crossing the rive in case 2:

that would be because of both gravity and friction. so     c

as we know our atmosphere or air have different levels. every level has other gasses, and every gas has another permeability. when the light comes from lower permeability to higher permeability, it changes its direction. so that means that when the light comes from the moon to the earth, it changes it's direction many more times. it basically means that the shape of the light part of the moon is changed on the earth.

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