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…”

Answer

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 base, and

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 to0 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

The rocket’s impulse is

.

Conclusion

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