# Thread: Vector problem

1. ## Vector problem

2. A boat is heading due east at 25 km/hr (relative to the
water). The current is moving toward the southwest at 10
km/hr.
(a) Give the vector representing the actual movement of
the boat.
(b) How fast is the boat going, relative to the ground?
(c) By what angle does the current push the boat off of
its due east course?

A - I don't I'm doing it right. I have 25i +10j + 26.9k
I used the Pythagorean theorem with a = 25 b = 10, and I solved for c.

b - I don't know how to deal with the southwest. It would be easy if the current was going in the opposite direction of the boat.

c- same. I don't know how to deal with the southwest direction.

Thanks!

2. Originally Posted by Truthbetold
2. A boat is heading due east at 25 km/hr (relative to the
water). The current is moving toward the southwest at 10
km/hr.
(a) Give the vector representing the actual movement of
the boat.
(b) How fast is the boat going, relative to the ground?
(c) By what angle does the current push the boat off of
its due east course?

A - I don't I'm doing it right. I have 25i +10j + 26.9k
I used the Pythagorean theorem with a = 25 b = 10, and I solved for c.

b - I don't know how to deal with the southwest. It would be easy if the current was going in the opposite direction of the boat.

c- same. I don't know how to deal with the southwest direction.

Thanks!
(a) $\displaystyle v = [25 - 10\cos(45^\circ)]\vec{i} - 10\sin(45^\circ)\vec{j}$

$\displaystyle v_x = 25 - 10\cos(45^\circ)$ ... $\displaystyle v_y = -10\sin(45^\circ)$

(b) $\displaystyle |v| = \sqrt{v_x^2 + v_y^2}$

(c) $\displaystyle \theta = \arctan\left(\frac{v_y}{v_x}\right)$

,

,

,

,

,

,

### a boat travels due east for a distance of 5.74 km and then travels 25 degrees south of east for a distance of 6.28 km. find the magnitude and direction (relative to due east) of the total displacement vector of the boat.

Click on a term to search for related topics.