How Does a Boat's Velocity Change When Pointing Upstream?

[Pius]

Homework Statement

a boat that can travel at 12.5 m/s on a lake goes 10.6 m/s when going straight up river (with respect to land) if the boat turns and heads (points) 22 degrees upstream from straight across the river. what is the boat's resultant velocity

Homework Equations

I don't know!

The Attempt at a Solution

I don't know!

Thanks for your help in advance!

 

[ideasrule]

Draw a vector diagram. Remember that since the boat can only travel 10.6 m/s instead of 12.5 m/s, the water in the river must be moving.

 

[kerimek]

I would approach this problem by first understanding the variables involved and their relationships. The boat's velocity on the lake is given as 12.5 m/s, and when going straight up river, it decreases to 10.6 m/s. This indicates that the river's current is pushing against the boat, causing a decrease in speed.

Next, we are given the angle at which the boat is pointing upstream, which is 22 degrees. This means that the boat's direction is not directly against the river's current, but at an angle.

To find the boat's resultant velocity, we can use vector addition. The boat's velocity on the lake can be represented as a vector pointing to the right with a magnitude of 12.5 m/s. The river's current can be represented as a vector pointing to the left with a magnitude of (12.5-10.6) m/s = 1.9 m/s.

Using trigonometry, we can find the magnitude of the boat's resultant velocity by using the given angle (22 degrees) and the magnitude of the river's current (1.9 m/s). This will give us the magnitude of the boat's resultant velocity as it moves upstream.

Finally, to find the direction of the boat's resultant velocity, we can use the same trigonometric principles to find the angle between the resultant velocity vector and the direction of the river's current. This will give us the direction in which the boat is moving with respect to the river's current.

In conclusion, to find the boat's resultant velocity, we need to use vector addition and trigonometric principles to find both the magnitude and direction of the velocity vector. This will give us a comprehensive understanding of the boat's motion on the river.