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Elza [17]
2 years ago
9

A rocket is launched straight up with constant acceleration. Four seconds after liftoff, a bolt falls off the side of the rocket

. The bolt hits the ground 6.30 seconds later. What is the acceleration of the rocket?
Physics
1 answer:
NARA [144]2 years ago
3 0

The constant acceleration of a rocket launched upward, calculated knowing that the time it takes for a bolt that falls off the side of the rocker was 6.30 seconds, is 5.68 m/s².                                                                                      

When the rocket is launched straight up with constant acceleration, the acceleration of the rocket is given by:

v_{f_{r}} = v_{i_{r}} + at    

Where:                                                              

v_{f_{r}}: is the final velocity of the rocket

v_{i_{r}}: is the initial velocity of the rocket = 0

a: is the acceleration

t: is the time

After 4 seconds, the <u>final speed of the rocket</u> will be the <u>initial speed of the bolt</u>, so:                                              

v_{f_{r}} = v_{i_{b}} = at = 4a  

When the bolt falls off the side of the rocket, the bolt hits the ground 6.30 seconds later.        

The<u> initial height of the bolt</u> will be the <u>final height of the rocket</u>, and vice-versa. With this, we can take the final height of the bolt as zero.                        

y_{f_{b}} = y_{i_{b}} + v_{i_{b}}t - \frac{1}{2}gt^{2}

0 = y_{i_{b}} + v_{i_{b}}t - \frac{1}{2}gt^{2}

y_{i_{b}} = \frac{1}{2}9.81*(6.30)^{2} - 4a*6.30 = 194.7 - 25.2a

Now, as we said above, this height (of the bolt) will be the final height of the rocket, so:

y_{f_{r}} = y_{i_{r}} + v_{i_{r}}t - \frac{1}{2}gt^{2}

194.7 - 25.2a = 0 + 0 - \frac{1}{2}a(4)^{2}    

a = \frac{194.7}{33.2} = 5.86 m/s^{2}    

   

Therefore, the acceleration of the rocket is 5.68 m/s².

You can find another example of acceleration calculation here: brainly.com/question/24589208?referrer=searchResults

I hope it helps you!                                                                              

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