A river has a current of 4 m/s south with respect to the shore. A swimmer is swimming in the river (which is redundant).
a. If the swimmer is swimming 2 m/s north with respect to the water, what is his velocity relative to the shore?
b. If the swimmer is swimming 3 m/s south with respect to the water, what is his velocity relative to the shore?
a) What is 4S+2N?
b) what is 4S+3S?
To solve these problems, we can use vector addition. The velocity of the swimmer relative to the shore is the sum of the velocity of the swimmer in the water and the velocity of the water current.
a. If the swimmer is swimming 2 m/s north with respect to the water, we can express the velocities as vectors. The velocity of the swimmer relative to the shore, V_s, is given by:
V_s = V_w + V_c
where V_w is the velocity of the swimmer in the water (2 m/s north) and V_c is the velocity of the water current (4 m/s south).
V_w = 2 m/s north
V_c = 4 m/s south
To add the vectors, we consider their directions. Adding the vectors will give us the resultant velocity of the swimmer relative to the shore.
V_s = V_w + V_c
V_s = 2 m/s north + (-4 m/s south)
V_s = 2 m/s north - 4 m/s south
V_s = -2 m/s south
Therefore, the swimmer's velocity relative to the shore is 2 m/s south.
b. If the swimmer is swimming 3 m/s south with respect to the water, we can use the same approach as before.
V_w = 3 m/s south
V_c = 4 m/s south
V_s = V_w + V_c
V_s = 3 m/s south + 4 m/s south
V_s = 7 m/s south
Therefore, the swimmer's velocity relative to the shore is 7 m/s south.
To find the swimmer's velocity relative to the shore, we need to consider both the velocity of the swimmer with respect to the water and the velocity of the water with respect to the shore. Let's break it down step by step:
a. Given:
Velocity of the river current with respect to the shore = 4 m/s south
Velocity of the swimmer with respect to the water = 2 m/s north
To find the swimmer's velocity relative to the shore, we can add the two velocities together. However, since the velocities are in opposite directions, we need to subtract them:
Swimmer's velocity relative to the shore = Velocity of the swimmer with respect to the water - Velocity of the river current with respect to the shore
Substituting the given values:
Swimmer's velocity relative to the shore = 2 m/s north - 4 m/s south
To subtract these velocities, we need to ensure they have the same direction. We can convert the south velocity to north by changing its sign:
Swimmer's velocity relative to the shore = 2 m/s north + 4 m/s north
Now we can add the two velocities together:
Swimmer's velocity relative to the shore = 6 m/s north
So, the swimmer's velocity relative to the shore is 6 m/s north.
b. Given:
Velocity of the river current with respect to the shore = 4 m/s south
Velocity of the swimmer with respect to the water = 3 m/s south
To find the swimmer's velocity relative to the shore, we use the same approach as before:
Swimmer's velocity relative to the shore = Velocity of the swimmer with respect to the water - Velocity of the river current with respect to the shore
Substituting the given values:
Swimmer's velocity relative to the shore = 3 m/s south - 4 m/s south
Again, to subtract these velocities, we need to ensure they have the same direction by changing their signs:
Swimmer's velocity relative to the shore = 3 m/s south + (-4 m/s south)
Now we can add the two velocities together:
Swimmer's velocity relative to the shore = -1 m/s south
So, the swimmer's velocity relative to the shore is 1 m/s south. Note that the negative sign indicates the direction is opposite to the shore, which means the swimmer is moving against the current.