Calculating Boat Speed Relative to Shore Observer in 2-D Motion

[krazykaci]

A boat crosses a river of width 134m in which the current has a uniform speed of 1.24m/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 2.62m/s relative to the water.

What is the magnitude of the speed of the boat relative to a stationary shore observer? anser in units of m/s


ok... if anyone can give me a clue on where to start i would love it!

~thanks

 

[berkeman]

Can you draw a vector diagram showing the velocity vector of the boat with respect to the water, and the vector for the velocity of the water? What do you do with these vectors to get the answer?

 

[kyle8921]

I would approach this problem by breaking it down into its components and using mathematical equations to solve for the desired information. To calculate the boat's speed relative to a stationary shore observer, we can use the Pythagorean theorem to find the resultant velocity.

First, we need to determine the boat's velocity relative to the water. This can be calculated by subtracting the current velocity from the boat's speed of 2.62m/s. So, the boat's velocity relative to the water is 2.62m/s - 1.24m/s = 1.38m/s.

Next, we can use the Pythagorean theorem to find the resultant velocity. The resultant velocity is equal to the square root of the sum of the squares of the boat's velocity relative to the water and the current velocity. So, the resultant velocity is √(1.38^2 + 1.24^2) = 1.81m/s.

Therefore, the magnitude of the boat's speed relative to a stationary shore observer is 1.81m/s. This means that if a person standing on the shore were to measure the boat's speed, they would observe it moving at 1.81m/s in a direction perpendicular to the river.

I hope this helps to guide you in solving similar problems in the future. Remember to always break down the problem into smaller components and use relevant equations to find the desired information.