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Byju's Answer

Standard XII

Physics

2nd Equation of Motion

A projectile ...

Question

A projectile is fired from the surface of earth of radius R with a speed $k v_{e}$ in radially outward direction (where $v_{e}$ is escape velocity and k < 1). Neglecting air resistance, the maximum height from the centre of the earth is:

\frac{R}{k^{2} + 1}

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\frac{R}{1 - k^{2}}

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k R

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k^{2} R

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Solution

The correct option is B $\frac{R}{1 - k^{2}}$
$K_{i} + U_{i} = K_{F} + U_{f} \Rightarrow \frac{1}{2} m k^{2} (\frac{2 G M}{R}) - \frac{G M m}{R} = 0 - \frac{G M m}{h} \Rightarrow h = \frac{R}{1 - k^{2}}$

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A projectile is fired from the surface of earth of radius R with a speed kve in radially outward direction (where ve is escape velocity and k < 1). Neglecting air resistance, the maximum height from the centre of the earth is:

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The correct option is B $\frac{R}{1 - k^{2}}$
$K_{i} + U_{i} = K_{F} + U_{f} \Rightarrow \frac{1}{2} m k^{2} (\frac{2 G M}{R}) - \frac{G M m}{R} = 0 - \frac{G M m}{h} \Rightarrow h = \frac{R}{1 - k^{2}}$