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goldenfox [79]
3 years ago
12

A model rocket blasts off from the ground, rising straight upward with a constant acceleration that has a magnitude of 85.0 m/s2

for 2.30 seconds, at which point its fuel abruptly runs out. Air resistance has no effect on its flight. What maximum altitude (above the ground) will the rocket reach?
Physics
1 answer:
sergey [27]3 years ago
6 0

Answer:

Maximum height attained by the model rocket is 2172.87 m

Explanation:

Given,

  • Initial speed of the model rocket = u = 0
  • acceleration of the model rocket = a\ =\ 85.0 m/s^2
  • time during the acceleration = t = 2.30 s

We have to consider the whole motion into two parts

In first part the rocket is moving with an acceleration of a = 85.0 m/s^2 for the time t = 2.30 s before the fuel abruptly runs out.

Let s_1 be the height attained by the rocket during this time intervel,

s_1\ =\ ut\ +\ \dfrac{1}{2}at^2\\\Rightarrow s_1\ =\ 0\ +\ 0.5\times 85\times 2.30^2\\\Rightarrow s_1\ =\ 224.825\ m

And Final velocity at that point be v

\therefore v\ =\ u\ +\ at\\\Rightarrow v\ =\ 0\ +\ 85.0\times 2.3\\\Rightarrow v\ =\ 195.5\ m/s.

Now, in second part, after reaching the altitude of 224.825 m the fuel abruptly runs out. Therefore rocket is moving upward under the effect of gravitational acceleration,

Let 's_2' be the altitude attained by the rocket to reach at the maximum point after the rocket's fuel runs out,

At that insitant,

  • initial velocity of the rocket = v = 195.5 m/s.
  • a = -g\ =\ -9.81\ m/s^2
  • Final velocity of the rocket at the maximum altitude = v_f\ =\ 0

From the kinematics,

v^2\ =\ u^2\ +\ 2as\\\Rightarrow 0\ =\ u^2\ -\ 2gs_2\\\Rightarrow s_2\ =\ \dfrac{u^2}{2g}\\\Rightarrow s_2\ =\ \dfrac{195.5^2}{2\times 9.81}\\\Rightarrow s_2\ =\ 1948.02\ m

Hence the maximum altitude attained by the rocket from the ground is

s\ =\ s_1\ +\ s_2\ =\ 224.85\ +\ 1948.02\ =\ 2172.87\ m

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