1) A model rocket is launched vertically from rest. The net acceleration is 17.5

Question

1) A model rocket is launched vertically from rest. The net acceleration is 17.5 m/s^2. After 1.5s, it runs out of fuel and its only acceleration is that of gravity.
a) ignoring air resistance, how high will the rocket go?
b) how much time after lunch will it take for the rocket to return to the ground?

2) Rocket from the previous problem has a mass of 87g and we can assume that the mass of the fuel is a lot smaller than 87g.
a) What is the net force exerted over the rocket during the first 1.5s after launch?
b) What force did the fuel exert on the rocket?
c) What was the net force over the rocket when the it ran out of fuel?
d) The vertial speed of the rocket reached 0 instantaneously at the highest point of its trajectory. What were the net forces and accelerations of the rockets in that instant?

Explanation / Answer

here,

1)

net accelration , a = 17.5 m/s^2

time , t = 1.5 s

when it ran out of fuel

h1 = 0 + 0.5 * a * t^2

h1 = 0.5 * 17.5 * 1.5^2 m

h1 = 19.7 m

the vertical speed , v1 = 0 + a * t

v1 = 26.25 m/s

a)

let the height be h

h - h1 = v1^2 /2 g

h - 19.7 = 26.25^2 /(2 * 9.81)

h = 54.8 m

b)

let the time taken to return to ground be t2

- h1 = v1 * t^2 - 0.5 * g * t2^2

- 19.7 = 26.25 * t2 - 0.5 * 9.81 * t2^2

t2 = 6.02 s

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