A spacecraft which is moving with a speed u r | vedclass

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(D) Initially,the velocity of the spacecraft with respect to the earth is $\vec{v}_{SE, i} = u \hat{i}$.The velocity of the planet with respect to the

Vedclass · Accepted Answer

$7u$

Vedclass · Answer

(D) Initially,the velocity of the spacecraft with respect to the earth is $\vec{v}_{SE, i} = u \hat{i}$.The velocity of the planet with respect to the earth is $\vec{v}_{PE} = -3u \hat{i}$.Therefore,the initial velocity of the spacecraft with respect to the planet is $\vec{v}_{SP, i} = \vec{v}_{SE, i} - \vec{v}_{PE} = u \hat{i} - (-3u \hat{i}) = 4u \hat{i}$.Since the planet is much more massive,the spacecraft undergoes an elastic collision in the planet's frame of reference. The magnitude of the velocity remains the same,but the direction is reversed. Thus,the final velocity of the spacecraft with respect to the planet is $\vec{v}_{SP, f} = -4u \hat{i}$.Finally,the velocity of the spacecraft with respect to the earth is $\vec{v}_{SE, f} = \vec{v}_{SP, f} + \vec{v}_{PE} = -4u \hat{i} + (-3u \hat{i}) = -7u \hat{i}$.The speed of the spacecraft with respect to the earth is $|\vec{v}_{SE, f}| = |-7u| = 7u$.

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