You are at Vertigo Amusement Park riding the new Vector roller coaster. The path of your...

You are at Vertigo Amusement Park riding the new Vector roller coaster. The path of your car is given by

where t = 0 corresponds to the beginning of your three-minute ride, measured in seconds, and spatial dimensions are measured in feet. It is a calm day, but after 90 sec of your ride your glasses suddenly fly off your face.

(a) Neglecting the effect of gravity, where will your glasses be 2 sec later?

(b) What if gravity is taken into account?