Question

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

Answer 1

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

Answer 2

v is slope of graph s-t
v(t) = s'(t) = -1920t + 26400
v(5) = -1920(5) + 26400