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Robert has just bought a new model rocket, and is trying to measure its flight characteristics. The rocket engine package claims that it will maintain a constant thrust of 12.3 N 12.3 N until the engine is used up. Robert launches the rocket on a windless day, so that it travels straight up, and uses his laser range‑finder to meaure that the height of the rocket when the engine cuts off is 10.2 m 10.2 m . He also measures the rocket's peak height, which is 14.7 m 14.7 m . If the rocket has a mass of 0.663 kg 0.663 kg , how much work is done by the drag force on the rocket during its ascent?

Answer :

Answer:

The work done by the drag force is given by 29.96 J

Explanation:

Given :

Thrust force [tex]F = 12.3[/tex] N

Displacement [tex]d = 10.2[/tex] m

Mass of rocket [tex]m = 0.663[/tex] Kg

From work energy theorem,

  [tex]W = \Delta K[/tex]

 [tex]W_{t} - Wd - W_{g} = KE[/tex]

Where [tex]W_{t} =[/tex] thrust work [tex]W_{g} =[/tex] gravitational work

[tex]KE = 12.3 \times 10.2 -Wd - 0.663 \times 9.8 \times 10.2[/tex]

[tex]KE = 59.2 -Wd[/tex]

After cutoff kinetic energy is converted into potential energy,

[tex]KE = Wd' + mg\Delta h[/tex]

Put value of KE

[tex]59.2 -Wd = Wd' + 0.663 \times 9.8 \times 4.5[/tex]

Work done by drag force is given by,

[tex]Wd'+Wd = 59.2 -29.23[/tex]

                 [tex]= 29.96[/tex] J

Therefore, the work done by the drag force is given by 29.96 J

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