22P3Q01

1a)

Inertia is a body’s resistance to change in motion (as quantified by its momentum). The larger the mass, the larger the inertia.

COMMENT: You should not write anything that gives the impression that mass and inertia are the same thing. You must not have the misconception that inertia is a kind of force.

1b)

\displaystyle \begin{aligned}   (g&=\frac{GM}{{{r}^{2}}}) \\  g&=\frac{(6.67\times {{10}^{-11}})(7.35\times {{10}^{22}})}{{{(1.74\times {{10}^{6}})}^{2}}} \\  &=1.62\text{ N k}{{\text{g}}^{-1}} \end{aligned}

COMMENT: This is a “show” question. So you must show all substitution value including \displaystyle 6.67\times {{10}^{-11}}.

1ci)

\displaystyle \begin{aligned}   (F&=v\frac{dm}{dt}) \\  10000&=v(70.0) \\  v&=143\text{ m }{{\text{s}}^{-1}} \end{aligned}

1cii)

After 15.0 s, mass\displaystyle \begin{aligned}   &=(4000-15.0\times 70.0) \\  &=2950\text{ kg} \\\end{aligned}

\displaystyle \begin{aligned}   ({{F}_{net}}&=ma) \\  10000-2950(1.62)&=(2950)a \\  a&=1.77\text{ m }{{\text{s}}^{-2}} \end{aligned}

1ciii)

The actual gravitational field strength decreases as the rocket travels away from the planet.

With a smaller downward weight, the net upward force would be larger. The actual acceleration is larger.

OR

After 15 s, the exhaust gases may be ejected from the rocket at a lower speed than that calculated in (c)(i). This implies a smaller thrust and a smaller acceleration.

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