Answer:
The recoil speed of the man and rifle is
.
Explanation:
The expression for the force in terms of mg is as follows;
F=mg
Here, m is the mass and acceleration due to gravity.
Rearrange the expression for mass.
![m=\frac{F}{g}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7BF%7D%7Bg%7D)
Calculate the combined mass of the man and rifle.
![m_{man,rifle}=\frac{650+25}{g}](https://tex.z-dn.net/?f=m_%7Bman%2Crifle%7D%3D%5Cfrac%7B650%2B25%7D%7Bg%7D)
Put
.
![m_{man,rifle}=\frac{650+25}{9.8}](https://tex.z-dn.net/?f=m_%7Bman%2Crifle%7D%3D%5Cfrac%7B650%2B25%7D%7B9.8%7D)
![m_{man,rifle}=68.88 kg](https://tex.z-dn.net/?f=m_%7Bman%2Crifle%7D%3D68.88%20kg)
The expression for the conservation of momentum is as follows as;
![m_{man}u_{man}+m_{bullet}u_{bullet}=m_{man}v_{man}+m_{rifle}v_{man,rifle}](https://tex.z-dn.net/?f=m_%7Bman%7Du_%7Bman%7D%2Bm_%7Bbullet%7Du_%7Bbullet%7D%3Dm_%7Bman%7Dv_%7Bman%7D%2Bm_%7Brifle%7Dv_%7Bman%2Crifle%7D)
Here,
is the mass of the man and rifle,
is the mass of the rifle,
are the initial velocities of the man and bullet and
are the final velocities of the man and rifle and rifle.
It is given in the problem that a rifle with a weight of 25 N fires a 4.5-g bullet with a speed of 240 m/s.
Convert mass of rifle from gram to kilogram.
![m_{bullet}=4.5 g](https://tex.z-dn.net/?f=m_%7Bbullet%7D%3D4.5%20g)
![m_{bullet}=.0045 kg](https://tex.z-dn.net/?f=m_%7Bbullet%7D%3D.0045%20kg)
Put
,
,
,
and
.
![m_{man}(0)+m_{bullet}(0)=(68.88)v_{man,rifle}+(.0045)(240)](https://tex.z-dn.net/?f=m_%7Bman%7D%280%29%2Bm_%7Bbullet%7D%280%29%3D%2868.88%29v_%7Bman%2Crifle%7D%2B%28.0045%29%28240%29)
![0=(68.88)v_{man,rifle}+(.0045)(240)](https://tex.z-dn.net/?f=0%3D%2868.88%29v_%7Bman%2Crifle%7D%2B%28.0045%29%28240%29)
![0=(68.88)v_{man,rifle}+1.08](https://tex.z-dn.net/?f=0%3D%2868.88%29v_%7Bman%2Crifle%7D%2B1.08)
![(68.88)v_{man,rifle}=\frac{-1.08}{68.88}](https://tex.z-dn.net/?f=%2868.88%29v_%7Bman%2Crifle%7D%3D%5Cfrac%7B-1.08%7D%7B68.88%7D)
Therefore, the recoil speed of the man and rifle is
.
Total mechanical energy: D) 2800 J
Explanation:
The total mechanical energy of an object is given by
![E=KE+PE](https://tex.z-dn.net/?f=E%3DKE%2BPE)
where:
is the kinetic energy of the object, which is the energy possessed by the object due to its motion, where
m = mass of the object
v = speed
And
is the gravitational potential energy of the object, the energy possessed by the object due to its location, where
is the acceleration due to gravity
h is the height of the object above the ground
For the body in this problem, we have:
m = 4.0 kg
v = 20 m/s
h = 50 m
Substituting, we find its total energy:
![E=\frac{1}{2}mv^2+mgh=\frac{1}{2}(4.0)(20)^2+(4.0)(9.8)(50)=2760 J \sim 2800 J](https://tex.z-dn.net/?f=E%3D%5Cfrac%7B1%7D%7B2%7Dmv%5E2%2Bmgh%3D%5Cfrac%7B1%7D%7B2%7D%284.0%29%2820%29%5E2%2B%284.0%29%289.8%29%2850%29%3D2760%20J%20%5Csim%202800%20J)
Learn more about kinetic and potential energy:
brainly.com/question/6536722
brainly.com/question/1198647
brainly.com/question/10770261
#LearnwithBrainly
From the calculation and the momentum of the body, the velocity is 62 m/s
<h3>What is momentum?</h3>
The term momentum refers to the product of mass and velocity. Now recall that the rate of change of momentum is equal to the impressed force.
Hence;
7440 kg-m/s = 120 kg * v
v= 7440 kg-m/s/120 kg
v = 62 m/s
Learn more about momentum:brainly.com/question/24030570
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