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.

1 Answer
Jul 19, 2018

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#