400,023 views
37 votes
37 votes
A 200 kg weather rocket is loaded with 100 kg of fuel and fired straight up. It accelerates upward at 34 m/s^2 for 35 s, then runs out of fuel. Ignore any air resistance effects. What is the rocket's maximum altitude? How long is the rocket in the air?

User Monkey Boson
by
2.4k points

1 Answer

15 votes
15 votes

Answer:

Maximum height = 93005 m

The total time of flight = 294 s

Step-by-step explanation:

The height during the burning:

s = ut + 0.5at^2

s = 0.5 x 34 x 35^2

s = 20825 m

End speed during the burn.

v = u + at = at

v = 34 x 35

v = 1190 m/s

It rises till the speed is zero:

v = u + at

t = (v - u)/a

t = -1190/-9.81

t = 121.3048 s

Maximum height = 20825 + 1190 x 121.308 - 0.5 x 9.81 x 121.3048^2 = Maximum height = 93005 m

Time taken to fall from height

s = 0.5at^2

t^2 = 2s/a

time = SQRT(2s/a) =

time = SQRT(2 x 93005/9.81)

Time = 137.7 s

Therefore the total time of flight = 35 +121.3048 + 137.7

Therefore the total time of flight = 294 s

User Yimin Rong
by
3.0k points