# Vectors and Components Question

1. Homework Statement

Use the components method to solve this problem.
A river is flowing at 1.75 m/s. The river is 820m wide. You are on a boat that is going dock on the other side of the river, and 940 m upstream. If you need to get to the other dock in 10 minutes, what must the speed of the boat be with respect to the water?

2. Homework Equations

$$d_{1}$$=$$d_{0}$$+$$\frac{1}{2}$$t($$V_{1}$$+$$V_{0}$$)

3. The Attempt at a Solution

Well i assumed that (as can be seen in my attached picture) the boat was moving in a diagonal direction, so I knew that it would be moving in both the "x" and "y" direction.

x

$$d_{1}$$=$$d_{0}$$+$$\frac{1}{2}$$t($$V_{1}$$+$$V_{0}$$)
940m= 0+$$\frac{1}{2}$$(600s)($$V_{1}$$+0)
3.13=$$V_{1}$$

y

$$d_{1}$$=$$d_{0}$$+$$\frac{1}{2}$$t($$V_{1}$$+$$V_{0}$$)
820m= 0+$$\frac{1}{2}$$(600s)($$V_{1}$$+1.75m/s)
.98=$$V_{1}$$

3.13+.98= 4.11m/s = $$V_{1}$$

Can someone please tell me if this method is correct?? If not, please explain. Thanks so much!

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