A rabbit runs across a parking lot on which a set of coordinate...?

Question

A rabbit runs across a parking lot on which a set of coordinate axes has strangely enough been drawn. The coordinates of the rabbit's position as functions of time are given by

$x = (- 0.31 \frac{m}{s^{2}}) t^{2} + (7.2 \frac{m}{s}) t + 28 m$ $x=(-0.31m/s^2)t^2+(7.2m/s)t+28m$
$y = (0.22 \frac{m}{s^{2}}) t^{2} + (- 9.1 \frac{m}{s}) t + 30 m$ $y=(0.22m/s^2)t^2+(-9.1m/s)t+30m$

a.) At t=15s, what is the rabbit's position vector r in unit vector notation and as a magnitude and an angle?

b.) Find the velocity v at time 15s in unit vector notation and as magnitude and angle.

15239 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-19T13:51:01

here they are

t=15

x=-69.7+108+28= $66.3 m$ $66.3m$

y=49.5-136.5+30= $- 57 m$ $-57m$

$\to r$ $vecr$ =66.3i-57j

| $\to r$ $vecr$ |= $sqrt(66.3²+57²)$ = $87.434m$

θ= $tan^-1$ $y/x$ = $-40^o$

$u_x$ = $dx/dt$ =-9.3+7.2= $-2.1$ $m/s$

$u_y$ = $dy/dt$ =6.6-9.1= $-2.5$ $m/s$

$vecu$ =-2.1i-2.5j

| $vecu$ |= $sqrt(2.1²+2.5²)$ = $3.265$ $m/s$

φ= $tan^-1$ $(uy)/(ux)$ = $230^o$