Question

1. A rocket is launched straight up with constant unknown acceleration a). A time t) after liftoff, a bolt breaks loose off near the bottom of the rocket. The bolt hits the ground a time (t) later. Therefore, the total ne from launch, to when the bolt hits the ground ist, + t a. State the type of motion while the bolt is attached to the rocket. b. State the type of motion after the bolt has fallen off of the rocket c. Sketch a diagram of the scenario. Make sure to include any relevant variables on the diagram. Indicate 3 events on the diagram that will be used to solve this problem. d. Discuss the concept you are going to use to find the acceleration of the rocket. This discussion should include what equations you will be using and the reason you can use those equations. Derive the equation for the acceleration of the rocket as a function of t, and t, This means you should end up with an equation consisting of a = equation with t, t, and numbers). Hints: i. You should treat t, and to as known variables. ii. Just after the bolt falls off the rocket, its velocity is not zero. It is the same as just before it fell off the rocket. iii. Just before the bolt hits the ground, the velocity is not zero, it is unknown. f Calculate the limit of the acceleration as to goes to zero for a constant finite ). Explain why this limit makes physical sense. g. Calculate the limit of the acceleration as to goes to infinity for a constant finite t.). Explain why this limit makes physical sense. We also want to know the thrust force required to lift the rocket h. Discuss the concept you are going to use to find the thrust force. This discussion should include what equations you will be using and the reason you can use those equations. i. Draw a free body diagram for the rocket Make sure to include labels for each force, a coordinate system and the direction of the acceleration. i. Find the equation for the thrust force of the rocket as a function of the rockets mass (m), & t, and to This means you should end up with an equation consisting of F = equation with m, g. t t and numbers). Continued on next page

Answer 1

A) when the bolt is attached to the rocket then the motion is linear as it is going in straight line path due  to the force of the gas when bolt is there the rocket is working correct and motion is a straight line as normal

B) but when the bolt is detached from the rocket , there is imbalance in the rocket and it will start falling down and the path followed during the fall is the parabolic.

ósbolt It V la=constant bolt stoke ~ the goound.

b) tot the acceleration of the pocket be'a' Velocity of the socket after time'ti' V= utat 50+a+ = at, This is obviusly disected upwards Now we have to calculate for the distance trovetted, s=utt fat² 8 = Oxt +į at = dat?

Speed of the bolt vaati a=-9 time =ta. Now s=utt at ² į at,' = (at) (tg) + 3x6-9.8) - at, ² = at, tz - 9.8 the atite + £at? = 9.8 t at , ( tz + + ( ) = 9,8 t ² ato (aby #ts) - que te a = 99 } **24,+8) Acceleration (a) = +, (2tg ++1)