Answer:
M=125 kg
v=1.75 m/s
Explanation:
From the law of linear momentum
P =mv
Case 1 50*V =M* 0.7 equation 1
50*V =(M+50)* 0.5 equation 2
equating 1 and 2
M* 0.7=(m+50)* 0.5
0.2 M= 25
M=125 kg
Putting value of M in equation 1
50*V =125*0.7
V=1.75 m/s
The mass of the boat is 125 kg
The speed of the person is 1.75 m/s
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Newton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.
[tex]\large {\boxed {F = ma }[/tex]
F = Force ( Newton )
m = Object's Mass ( kg )
a = Acceleration ( m )
Let us now tackle the problem !
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Given:
mass of person = m_p = 50 kg
final speed of the boat in first case = v_{b1} = 0.70 m/s
final speed of the boat in second case = v_{b2} = 0.50 m/s
Asked:
mass of boat = m_b = ?
speed of the person = v_p = ?
Solution:
We will use Conservation of Momentum Law as follows:
First Case:
[tex]m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2[/tex]
[tex]m_pu_p + m_bu_b = m_pv_p + m_bv_{b1}[/tex]
[tex]50(0) + m_b(0) = -50v_p + m_b(0.70)[/tex]
[tex]0 = -50v_p + 0.70m_b[/tex]
[tex]50v_p = 0.70m_b[/tex]
[tex]m_b = \frac{500}{7} v_p[/tex] → Equation A
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Second Case:
[tex]m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2[/tex]
[tex]m_pv_p + m_bu_b = (m_p + m_b)v_{b2}[/tex]
[tex]50v_p + m_b(0) = (50 + m_b)(0.50)[/tex]
[tex]50v_p = (50 + m_b)(0.50)[/tex]
[tex]100v_p = (50 + m_b)[/tex]
[tex]100v_p = 50 + \frac{500}{7} v_p[/tex] ← Equation A
[tex]100v_p - \frac{500}{7} v_p = 50[/tex]
[tex]\frac{200}{7}v_p = 50[/tex]
[tex]v_p = \frac{7}{4} \texttt{ m/s}[/tex]
[tex]v_p = 1.75 \texttt{ m/s}[/tex]
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[tex]m_b = \frac{500}{7} v_p[/tex]
[tex]m_b = \frac{500}{7}(1.75)[/tex]
[tex]m_b = 125 \texttt{ kg}[/tex]
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Grade: High School
Subject: Physics
Chapter: Dynamics
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Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant
