Answer to Question #95482 in Mechanics | Relativity for colin

Question

A snowmobile is originally at the point with position vector 28.5 m at 95.0° counterclockwise from the x axis, moving with velocity 4.69 m/s at 40.0°. It moves with constant acceleration 1.85 m/s2 at 200°. After 5.00 s have elapsed, find the following. (Express your answers in vector form.)

Answer 1

After 5 seconds velocity is given by

$\overset{\to}{v}=\overset{\to}{u}\ +\ 5\overset{\to}{a}$

Talking about components

$v_x=u_x\ +\ 5a_x\\v_y=u_y\ +\ 5a_y$

$v_x=4.69\cos(40\degree)+5\times1.85\cos(200\degree)\\v_y=4.69\sin(40\degree)+5\times 1.85\sin(200\degree)$

$v_x=-5.098\\v_y=-0.149\\|v|=\sqrt{v_x^2+v_y^2}=5.1\ m\ sec^{-1}$

$\tan(\theta)=\frac{0.149}{5.098}=0.0292\\\theta=1.67\\since \ both\ component\ are\ negative\ so angle \ will\ be\ 180+1.67=181.67\degree$ So velocity after 5 seconds is elapsed will be

$5.1\ m\ sec^{-1}$ at an angle of $181.67\degree$

Or in term of vector component

$\overset{\to}{v}=-5.098\hat{i}-0.149\hat{j}$