Work and solutions please and thank you! Open -Response Homework Problem 10.1 A

Question

Work and solutions please and thank you!

Open -Response Homework Problem 10.1 A certain lb hunting rifle fires a 1S0 grain bullet at a target 1000 yds away. The bullet experiences an acceleration of ?2.7* (opposite direction of velocity) due to air resistance. When the bullet hits the target, its velocity is measured to be S20 . Express all answers in SI units. Helpful conversions: 1 grain = 6.48 x 10^-5kg un = 3.281 ft a mass of lkg weighs 2.2075 pounds (at the surface of the earth) (a)[3 pt(s) 'What is the rifle's muzzle velocity (the velocity the bullet has as it leaves the rifle barrel)? (b)[2 pt(s)_]What is the recoil velocity of the rifle? (c)(2 pt(s) 'Neglecting energy lost to heat and the rotation of the bullet, how much internal energy was required to fire the bullet? (d)[3 pt(s) '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

Part A)

First we need the initial velocity of the bullet as it left the rifle...

1000 yards converts to 914.4 m

vf2 = vo2 + 2ad

(820)2 = vo2 + 2(-2.7)(914.4)

vo = 823 m/s

Part B)

Then by conservation of momentum

mv = mv

mass of the rifle ... 8 lb = 3.62874 kg

mass of the bullet (180)(6.48 X 10-5) = .011664 kg

(3.62874)v = (.011664)(823)

v = 2.65 m/s

Part C)

E = .5mv2

E = (.5)(.011664)(823)2

E = 3950 J

Part D)

We need the time to travel the 1000 m

vf = vo + at

820 = 823 + (-2.7)(t)

t = 1.11 sec

Then in the vertical direction

d = vot + .5at2

d = 0 + .5(9.8)(1.11)2

d = 6.05 m

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