Respuesta :
Answer:
(a) Speed of baseball is 31.03 m/s
(b) Bullet has greater kinetic energy than baseball
Explanation:
Given :
Mass of baseball, M = 0.145 kg
Mass of bullet, m = 3 g = 3 x 10⁻³ kg
Speed of bullet, v = 1.50 x 10³ m/s
Let u m/s be the speed of the baseball.
(a)
According to the problem, momentum of bullet and momentum of baseball is same. So,
M x u = m x v
[tex]u=\frac{m\times v}{M}[/tex]
Substitute the values of m, M and v in the above equation.
[tex]u=\frac{3\times10^{-3}\times1.50\times10^{3} }{0.145}[/tex]
u = 31.03 m/s
(b) Kinetic energy of baseball is given by the relation :
[tex]K_{1}=\frac{1}{2} Mv^{2}[/tex]
Substitute the values of M and v in the above equation. [tex]K_{1}=\frac{1}{2} \times 0.145\times(31.03)^{2}[/tex]
K₁ = 69.80 J
Kinetic energy of bullet is given by the relation :
[tex]K_{2}=\frac{1}{2} m u^{2}[/tex]
Substitute the values of M and v in the above equation.
[tex]K_{2}=\frac{1}{2}\times3\times10^{-3}\times(1.50\times10^{3} )^{2}[/tex]
K₂ = 3375 J
Since, K₂ is greater than K₁, hence bullet has greater kinetic energy than baseball.
The velocity of the ball must be 31.096 m/s to validate the claim of the pitcher.
What is Momentum?
The momentum is defined as the product of the mass and velocity of an object.
[tex]P = mv[/tex]
Where,
[tex]p[/tex]- momentum
[tex]m[/tex] - mass
[tex]v[/tex] - velocity
Since both the ball and bullet has the same momentum,
So,
[tex]p_1 = p_2[/tex]
Where,
P_1 - momentum of the ball
p_2 - momentum of the bullet
Put the values in the formula,
[tex]{\rm 0.145 kg \times} v = 3{ \rm \ g \times 1.503\times 10^3}} \\\\v = {\rm \dfrac { 0.003 \ Kg \times 1.503\times 10^3 }{0.145 \ kg}}\\\\v = 31.096 \rm m/s[/tex]
Therefore, the velocity of the ball must be 31.096 m/s to validate the claim of the pitcher.
Learn more about Momentum:
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