Noah wants to swim across a river 10 m wide, flowing from north to south. He swims so his velocity with respect to the river is 2 m/s due east, and the river moves at 4 m/s. How far downstream in m from his starting point will he reach the other side?
tan A = Y/x = -4/2 = -2.0
A = -63.43o = 63.43o South of East.
tan(-63.43) = d/10m
d = 10*tan(-63.43) = -20 m = 20 m. South
of starting point.
To find out how far downstream Noah will reach the other side of the river, we can break down the problem into two components: Noah's velocity relative to the river and the river's velocity.
First, let's analyze Noah's velocity relative to the river. We are given that Noah swims with a velocity of 2 m/s due east. Since the river's flow is from north to south, we need to find the eastward component of Noah's velocity relative to the river. We can use vector addition to find this component.
Let's assume Noah's velocity relative to the river is represented by vector A and the river's velocity is represented by vector B. The eastward component of Noah's velocity relative to the river can be found using the formula:
Eastward component = magnitude of A * cos(theta)
Here, the magnitude of A is 2 m/s and theta is the angle between vectors A and B. Since A is due east and B is north to south, the angle between them is 90 degrees.
Let's calculate the eastward component:
Eastward component = 2 m/s * cos(90 degrees)
= 2 m/s * 0
= 0 m/s
Therefore, Noah's eastward velocity relative to the river is 0 m/s, which means he is only moving directly across the river. His velocity does not contribute to his downstream movement.
Now, let's consider the river's velocity. We are given that the river flows at 4 m/s. Since Noah's eastward velocity relative to the river does not contribute to his downstream movement, we only need to consider the river's velocity.
The downstream movement can be calculated by multiplying the river's velocity by the time taken to cross the river. To find the time taken to cross the river, we need to divide the width of the river by Noah's velocity relative to the river.
Time taken to cross the river = width of the river / velocity relative to the river
= 10 m / 2 m/s (since Noah's eastward velocity is 0 m/s)
= 5 s
Now, let's calculate the downstream distance:
Downstream distance = river's velocity * time taken to cross the river
= 4 m/s * 5 s
= 20 m
Therefore, Noah will reach a point 20 meters downstream from his starting point on the other side of the river.