A boat crosses a river of width 113 m in which
the current has a uniform speed of 0.933 m/s.
The pilot maintains a bearing (i.e., the direction in which the boat points) perpendicular
to the river and a throttle setting to give a
constant speed of 2.58 m/s relative to the water.
What is the magnitude of the speed of the
boat relative to a stationary shore observer?
How far downstream from the initial position
is the boat when it reaches the opposite shore?
speedboat^2=.933^2+2.58^2
time across: 113m/2.58m/s
downstream distance along river: .933*timeacross
Thank you! :)
To calculate the magnitude of the speed of the boat relative to a stationary shore observer, we need to consider the vector addition of the boat's speed relative to the water and the speed of the river current.
First, let's calculate the speed of the boat relative to the water using the speed and direction information provided.
The boat's speed relative to the water is given as 2.58 m/s, and the direction is perpendicular to the river. Since the boat is moving perpendicular to the river, its speed relative to the river current will not be affected.
Next, let's consider the speed of the river current, which is given as 0.933 m/s. Since the boat's movement is perpendicular to the river, the current will not directly affect the boat's speed relative to a stationary shore observer.
Therefore, the magnitude of the speed of the boat relative to a stationary shore observer is the same as the speed of the boat relative to the water, which is 2.58 m/s.
To calculate the distance downstream from the initial position when the boat reaches the opposite shore, we need to determine the time it takes for the boat to cross the river.
The time it takes for the boat to cross the river can be obtained by dividing the width of the river by the speed of the boat relative to the water:
Time = distance / speed = 113 m / 2.58 m/s
Calculating this, we get:
Time = 43.797 s
Since the boat is moving perpendicular to the river's current, the boat does not drift downstream during the crossing. Therefore, the boat will be at the opposite shore when it finishes crossing.
Hence, the boat will be 113 meters downstream from its initial position when it reaches the opposite shore.