Spaceship of mass m moves in the positive X-direction with speed c u(t) = 32+ct where a > 0 is a constant with dimensions of length. Does this speed ever exceed the speed of light? (a) What is the force, F(t), acting on the spaceship as a function of time? (b)
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Does this speed ever exceed the speed of light? The speed of light is denoted by 'c' and the spaceship's speed is given by u(t) = 32+ct. We know that the speed of light is a constant and is equal to 299,792,458 m/s. Therefore, the spaceship's speed will exceed Show moreā¦
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A constant force, acting for $3.6 \times 10^{4} \mathrm{s}(10 \mathrm{h}),$ brings a spaceship of mass $2200 \mathrm{kg}$ from rest to speed $0.70 c$ (a) What is the magnitude of the force? (b) What is the initial acceleration of the spaceship? Comment on the magnitude of the answer.
As $\vec{F}=0$, from the equation of dynamics of a body with variable mass; $$ m \frac{d \vec{v}}{d t}=\vec{u} \frac{d m}{d t} \text { or, } d \vec{v}=\vec{u} \frac{d m}{m} $$ Now $d \vec{v} \uparrow \downarrow \vec{u}$ and since $\vec{u} \perp \vec{v}$, we must have $|d \vec{v}|=v_{0} d \alpha$ (because $v_{0}$ is constant) where $d \alpha$ is the angle by which the spaceship turns in time $d t$. So, or,
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