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xeze [42]
3 years ago
13

After a 50-kg person steps from a boat onto the shore, the boat moves away with a speed of 0.70 m/s with respect to the shore. I

f the same person steps from the shore onto the boat, the person and the boat move away from the shore with the speed of 0.50 m/s. Assume that the initial speed of the person with respect to the shore is the same in both cases and that the person is moving in a horizontal direction. Determine the Mass of the boat and the speed of the person.

Physics
2 answers:
Svetradugi [14.3K]3 years ago
7 0

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

                   

KATRIN_1 [288]3 years ago
5 0

The mass of the boat is 125 kg

The speed of the person is 1.75 m/s

\texttt{ }

<h3>Further explanation</h3>

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.

\large {\boxed {F = ma }

F = Force ( Newton )

m = Object's Mass ( kg )

a = Acceleration ( m )

Let us now tackle the problem !

\texttt{ }

<u>Given:</u>

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

<u>Asked:</u>

mass of boat = m_b = ?

speed of the person = v_p = ?

<u>Solution:</u>

<em>We will use </em><em>Conservation of Momentum Law </em><em>as follows:</em>

<u>First Case:</u>

m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2

m_pu_p + m_bu_b = m_pv_p + m_bv_{b1}

50(0) + m_b(0) = -50v_p + m_b(0.70)

0 = -50v_p + 0.70m_b

50v_p = 0.70m_b

m_b = \frac{500}{7} v_p → <em>Equation A</em>

\texttt{ }

<u>Second Case:</u>

m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2

m_pv_p + m_bu_b = (m_p + m_b)v_{b2}

50v_p + m_b(0) = (50 + m_b)(0.50)

50v_p = (50 + m_b)(0.50)

100v_p = (50 + m_b)

100v_p = 50 + \frac{500}{7} v_p ← <em>Equation A</em>

100v_p - \frac{500}{7} v_p = 50

\frac{200}{7}v_p = 50

v_p = \frac{7}{4} \texttt{ m/s}

v_p = 1.75 \texttt{ m/s}

\texttt{ }

m_b = \frac{500}{7} v_p

m_b = \frac{500}{7}(1.75)

m_b = 125 \texttt{ kg}

\texttt{ }

<h3>Learn more</h3>
  • Impacts of Gravity : brainly.com/question/5330244
  • Effect of Earth’s Gravity on Objects : brainly.com/question/8844454
  • The Acceleration Due To Gravity : brainly.com/question/4189441
  • Newton's Law of Motion: brainly.com/question/10431582
  • Example of Newton's Law: brainly.com/question/498822

\texttt{ }

<h3>Answer details</h3>

Grade: High School

Subject: Physics

Chapter: Dynamics

\texttt{ }

Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant

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