A bullet of mass $10 g$ is fired horizontally with a velocity $1000 m s^{- 1}$ from a rifle situated at a height $50 m$ above the ground. If the bullet reaches the ground with a velocity $500 m s^{- 1}$ , the work done against air resistance in the trajectory of the bullet is (take $g = 10 m^{- 2}$ ).

$5005 J$

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$3755 J$

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$3750 J$

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$17.5 J$

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Solution

The correct option is B
$3755 J$

Step 1: Given data
Mass of bullet, $m = 10 g$
$1 g = 10^{- 3} K g m = 10 \times 10^{- 3} K g m = 10^{- 2} K g$
The initial velocity of the bullet, $u = 1000 m / s$
The final velocity of the bullet, $v = 500 m / s$
Height of riffle, $h = 50 m$
Step 2: Find the work done against air resistance
Work done against the air resistance is the energy lost
$W = m g h + \frac{1}{2} m u^{2} - \frac{1}{2} m v^{2} W = 10 m / s^{2} x 10^{- 2} K g x 50 m + \frac{1}{2} \times 10^{- 2} K g \times ({(1000 m / s)}^{2} - {(500 m / s)}^{2}) W = 3755 J$
Hence, option B is correct.

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A bullet of mass 10g is fired horizontally with a velocity 1000ms-1 from a rifle situated at a height 50m above the ground. If the bullet reaches the ground with a velocity500ms-1, the work done against air resistance in the trajectory of the bullet is (take g=10m-2).