Question

Upward velocity of a rocket can be computed by the formula...

Answer 1

BISECTION METHOD

v=uln(m₀/(m₀-qt))-gt.

Let f(t)=v-uln(m₀/(m₀-qt))+gt

A graph shows that the solution is in the interval [30,35], so initial values of a and b could be (a,b)=(30,35). The table shows consecutive iterations of a and b. The sign of the last column determines whether a or b has to be adjusted to the average value. If it’s negative, b has to be adjusted, and if positive, a has to be adjusted. The last row takes us up to the error margin of 0.00001, so t=33.04400 seconds.

Now we check using the original equation:

v=2200ln(160000/(160000-2680(33.044)))-9.8(33.044),

v=1449.99968m/s.