# Vector problem

• Oct 3rd 2010, 02:50 PM
Truthbetold
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!
• Oct 3rd 2010, 03:03 PM
skeeter
Quote:

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

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

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

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