# Math Help - Vectors

1. ## Vectors

Thanks, I am having a little trouble...

1.A ship is travelling @ 12 m/s. A passenger walks towards the back at 5 m/s. After walking for 2 sec, he then walks at the same speed at right angles to the direction of the ship for 2 secs.

Relative to the water:

a. What is the velocity in each case
b. What is the displacement in each case

2.A ship travelling @ 46km/hr aiming at the direction 124 T is pulled off course by a current of 8 km/hr in the direction 223 T. Find actual speed and direction of ship.

THanks for the help!

2. Originally Posted by classicstrings
Thanks, I am having a little trouble...

1.A ship is travelling @ 12 m/s. A passenger walks towards the back at 5 m/s. After walking for 2 sec, he then walks at the same speed at right angles to the direction of the ship for 2 secs.

Relative to the water:

a. What is the velocity in each case
b. What is the displacement in each case
(I'm not sure if you want it written in terms of i j and k but i'll do it anyway)
a. the boat is moving with a vector of $12\bold{i}$
the man is moving with a vector of $\neg5\bold{i}$
therefore the vector that shows his movemant relative to the water is:

$12\bold{i}+\neg5\bold{i}=12\bold{i}-5\bold{i}=\boxed{7\bold{i}}$

therefore his velocity is 7m/s

therefore his displacement after 2 sec is... $7\times2=14$ metres

b.the boat is moving with a vector of $12\bold{i}+0\bold{j}$
the man is moving with a vector of $0\bold{i}+5\bold{j}$
therefore the vector that shows his movemant relative to the water is:

$12\bold{i}+5\bold{j}$

therefore his velocity is...
$v=\sqrt{12^2+5^2}$

$v=\sqrt{144+25}$

$v=\sqrt{169}$

$\boxed{v=13}$m/s

therefore his displacement after 2 sec is... $13\times2=26$ metres

~ $Q\!u\!i\!c\!k$

3. ## A question of my own

Originally Posted by classicstrings
2.A ship travelling @ 46km/hr aiming at the direction 124 T is pulled off course by a current of 8 km/hr in the direction 223 T. Find actual speed and direction of ship.
What is "T"

4. I meant degrees true, but thanks I have worked out the 2nd one. Cheers!