Two meteoroids are heading for earth. their speeds as they cross the moon's orbit are 1.0 km/s .

Asked by maham237 @ 23/12/2020 in Physics viewed by 358 People

Two meteoroids are heading for earth. their speeds as they cross the moon's orbit are 1.0 km/s . part a the first meteoroid is heading straight for earth. what is its speed of impact?

Answered by maham237 @ 23/12/2020

Answer : $v_{2} = 11.2\ km/s$

Explanation : The total energy of the meteoroids

Total Energy = Kinetic Energy + Potential Energy

$E = \dfrac{1}{2}mv^{2} - \dfrac{GMm}{R}$

Total energy remain constant.

Now, for both meteoroids

$\dfrac{1}{2}m(v_{2}^{2} - v_{1}^{2}) = GMm\left(\dfrac{1}{R}-\dfrac{1}{r}\right)$

Where, R = radius of the earth

r = distance of the moon

M = mass of the earth

m = mass of the meteoroid

$v_{2}^{2} = 2GM\left(\dfrac{1}{R}-\dfrac{1}{r}\right)+ v_{1}^{2}.....(I)$

Now, put the values in equation (I)

$v_{2}^{2} = 1 + 2\times6.67\times10^{-11}\times6\times10^{24}\left(\dfrac{1}{6.37} - \dfrac{1}{384}\right)\times10^{-6}$

$v_{2}^{2} = 12361\times 10^{4}\ m/s$

$v_{2} = 11118.003\ m/s$

$v_{2} = 11.2\ km/s$

Hence, this is the required solution.

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