Question

Application of integration problem

Answer 1

i need help for part d.
a.) m(t)=-20t^2+500
b.)5min
c.)6 km
d.) i now we need to do integration but im unsure of the equation

Answer 2

You will be integrating from the time he lift off and the time the bag ran out of candy. So initial time would be t=0. The find the final time you need to solve for t from equation a. Set m = 0 and the solve for t. Set m=0 because all the candy has emptied out so no mass. That will give you the final time t. Work is F*d and Force is mg since you are given gravity.
Work includes the sleigh, Santa and the candy and the only that changes is the mass.
\[\int\limits_{0}^{t} (Ag) (1500 -40t)dt\]

A = altitude
g= gravity constant
Integrate with respect to t.
The mass m is given by the function for time.