The height of a balloon is given by the fucntion

s (t) = - 960t^2+26400t, where t = hours since lift-off and s = feet. Find the velocity of the balloon 5 hours after lift off

16800 metres

Working

i) Differentiate the given function to get the velocity function:

ds/dt = = 1920t + 26400

Then replace the value of t with 5 hours

v (t) = - 1920 (5) + 26500

v (t) = - 9600+26500

V (5) = 16800 m

V is slope of graph s-t

v (t) = s' (t) = - 1920t + 26400

v (5) = - 1920 (5) + 26400