A certain 8lb hunting rifle fires a 180 grain bullet at a target 1000yds away. T

Question

A certain 8lb hunting rifle fires a 180 grain bullet at a target 1000yds away. The bullet experiences an acceleration of -2.7 m/s^ 2 (opposite direction of velocity) due to air resistance. When the bullet hits the target, its velocity is measured to be 820 m s . Express all answers in SI units. Helpful conversions:

1 grain = 6.48 x 10^-5 kg 1m = 3.281ft

a mass of 1kg weighs 2.2075 pounds (at the surface of the earth)

Assuming the bullet leaves the gun with a perfectly horizontal velocity, and that the air resistance is also horizontal, how far has the bullet fallen when it hits the target?

Explanation / Answer

Here ,

distance , d = 1000 yards,

d = 914.4 m

a = -2.7 m/s^2

intial speed , u = 820 m/s

Now, for time to reach the target t

using second equation of motion

d = u*t + 0.5 * at^2

914.4 = 820 * t -0.5 * 2.7 *t^2

solving for t

t = 1.117 s

Now, for height dropped ,

h = 0.5 * gt^2

h = 0.5 * 9.8 * 1.117^2

h = 6.113 m

the height dropped by the bullet is 6.113 m

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