**Far in space, where gravity is negligible, a 440 kg rocket traveling at 75 m/s fires itsengines. Figure P9.26 shows the…**

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## Question “Far in space, where gravity is negligible, a 440 kg rocket traveling at 75 m/s fires itsengines. Figure P9.26 shows the…”

traveling at 75 m/s fires itsengines. Figure P9.26 shows the thrust

force as a function of time,with the horizontal axis in 11

sincrements. The mass lost by the rocket during these 33 s is

negligible.

therocket?

N

**Â·**s

(b) At what time does the rocket reach its maximum speed?

s

What is the maximum speed?

m/s

## Answer

Impulse momentum theorem and other concepts are used to solve this problem.

The impulse-momentum theory theorem states that impulse is equal to area under force time graph.

To find out the speed at which the rocket can reach its maximum speed, use the impulse momentum theorem.

Finally, use the impulse momentum relation to determine the maximum speed.

Impulse is a contraction of

acts as the impulse, #media_tag_2$ is the force, @media_tag_3$ is the initial time and @media_tag_4$ the final.

The impulse equals the area under the $5$ curve (

).

The expression for the area of the triangle is:

*A* here is the Area of the Triangle,

the height.

The area under the force graph is the impulse that is caused by a force.

Expression of impulse is:

…… (1)

The impulse momentum theorem.

The impulse applied to an object is equal to the change in momentum.

…… (2)

Momentum is the sum of velocity and mass.

represents the momentum, #media_tag_15$ the mass, and @media_tag_16$ the velocity.

You can write the initial momentum as:

provides the initial momentum and

the initial velocity.

The final momentum can be described as:

represents the final momentum and

the final velocity.

Substituting HTMLmedia_tag_23$ or HTMLmedia_tag_24$ into (2).

Rearranging the equation above will allow you to:

The final momentum can be described as:

…… (3)

Also, the expression for maximum speed would be:

…… (4)

**(a)**

The rocket’s impulse is described as,

Substitute HTMLmedia_tag_29$ to

or HTMLmedia_tag_31$ to

.

**(b.1)**

The rocket’s motion in space is controlled by no force. The thrust force from the engine is the only force that acts on it.

The given force vs. time graph.

The rocket accelerates from *to*0 to *t=*33. This is until *_t=*33.

The rocket’s maximum speed is *t=*33 S.

Because the rocket keeps pushing until it stops, it reaches its maximum speed at

.

**(b.2)**

The final momentum can be described as:

The expression for maximum speed, as derived from the above, is:

Substitute

to

;

to

and

to

.

Ans: Part A

**.**

## Conclusion

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