91影视

The asteroid travels with constant speed of $20\mathrm{km}/\mathrm{s}$.

Its distance from the Earth is $4.0脳{10}^6\mathrm{km}$.

If the mission fails, the time taken by the asteroid to hit the Earth is given by

$t=\frac{\text{Distance}}{\text{Speed}}=\frac{4.0脳{10}^6\mathrm{km}}{20\frac{\mathrm{km}}{\mathrm{s}}}=2.0脳{10}^5\mathrm{s}$

$t=2.0脳{10}^5搂脳\frac{1h}{3600蠒}=55.56h鈮�56h$

If the mission fails, it takes $56h$by the asteroid to hit the Earth.

The distance of the asteroid from Earth is $4.0脳{10}^6\mathrm{km}$.

The radius of the Earth is $6400\mathrm{km}$.

The minimum angle of deflection to miss the Earth is given by

$胃={\tan }^{-1}\left(\frac{6400\mathrm{km}}{4.0脳{10}^6\mathrm{km}}\right)=0.092掳$

The minimum angle must the asteroid be deflected to just miss the earth is $0.{092}^o$.

Initially there is no horizontal motion. After the rocket is fired, there is an acceleration along the horizontal direction

The initial horizontal velocity is zero.

The horizontal velocity of the asteroid after $300\mathrm{s}$ is given by

The vertical velocity of the asteroid is constant and given by $v_y=20000\mathrm{m}.{\mathrm{s}}^{-1}$.

The angle of deflection due to horizontal velocity is given by

Since this angle is greater than the angle of minimum deviation, Earth is saved.

This angle is greater than the angle of minimum deviation, Earth is saved.