Question

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

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=(-0.31m/s^2)t^2+(7.2m/s)t+28m`
`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.

Answer 1

here they are

Explanation:

t=15

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

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

`vecr`=66.3i-57j

|`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`