Answer:
V = 3.97 m/s
Explanation:
Mass of a man, M = 85 kg
Mass of a bullet, m = 8 g = 0.008 kg
Speed of bullet, v = 410 m/s
We need to find the speed of a man in order to have the same kinetic energy as that of the bullet. Let the kinetic energy of the bullet is k. So,
[tex]k=\dfrac{1}{2}mv^2\\\\k=\dfrac{1}{2}\times 0.008\times 410^2\\\\k=672.4\ J[/tex]
Since, k = K (K is the kinetic energy of the man and Let V is the speed)
[tex]K=\dfrac{1}{2}MV^2\\\\V=\sqrt{\dfrac{2K}{M}} \\\\V=\sqrt{\dfrac{2\times 672.4}{85}} \\\\V=3.97\ m/s[/tex]
So, the speed of the man is 3.97 m/s.
We have that for the Question "How fast would a(n) 85 kg man need to run in order to have the same kinetic energy as an 8.0 g bullet fired at 410 m/s?" it can be said that the speed is
v=4.0m/s
From the question we are told
How fast would a(n) 85 kg man need to run in order to have the same kinetic energy as an 8.0 g bullet fired at 410 m/s?
Generally the equation for the kinetic energy is mathematically given as
[tex]K.E=1/2*m*v^2\\\\Therefore\\\\K.E=1/2*0.008*(420)^2\\\\K.E=672.4J\\\\[/tex]
Therefore
[tex]v^2=\frac{672.4*2}{85}\\\\v^2=15.821[/tex]
v=4.0m/s
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