vector angles

• Aug 30th 2008, 12:58 PM
Allie
vector angles
A child walks due east on the deck of a ship at 4 miles per hour.
The ship is moving north at a speed of 16 miles per hour.
Find the speed and direction of the child relative to the surface of the water.
Speed = mph
The angle of the direction from the north

I don't know what angle to find but i found the speed to be 16.4924
• Aug 30th 2008, 01:07 PM
Chris L T521
Quote:

Originally Posted by Allie
A child walks due east on the deck of a ship at 4 miles per hour.
The ship is moving north at a speed of 16 miles per hour.
Find the speed and direction of the child relative to the surface of the water.
Speed = mph
The angle of the direction from the north

I don't know what angle to find but i found the speed to be 16.4924

The speed looks right.

I assume you came up with the vector equation $\bold v=4\bold i+16\bold j$

Thus, $\parallel \bold v\parallel=\sqrt{16^2+4^2}\approx\color{red}\boxed {16.49}$

Now, to find the angle, use $\vartheta=\tan^{-1}\left(\frac{v_y}{v_x}\right)$, where $v_y~and~v_x$ are the y and x components of vector $\bold v$.

Does this make sense?

--Chris
• Aug 30th 2008, 01:11 PM
Allie
yes it does thank you i had the equation upside down