Students are testing their new drone to see if it can safely deliver packages to different departments on campus. Position data can be approximated using the expressions

x(t) = −0.0000225t^4+0.003t^3+0.01t^2 and y(t) = 300(1−cos(π/40t))
where x and y are expressed in meters and t is expressed in seconds. Assume that the take-off and landing altitudes are the same. Please note that that x is the horizontal axis and y is the vertical axis.

(a) Determine the duration of the flight. in seconds
(b) Determine its maximum speed in the x direction. in m/s
(c) Determine its maximum altitude and the horizontal distance traveled during the flight.