Ask question

Ask question

All categories

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.

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

You might be interested in

When is the next total solar eclipse in illinois

atroni [7]

April 8, 2024

Eclipse will be total over the southern part of the state. Roughly everything south of Decatur and Springfield.

7 0

3 years ago

What is work please give ans

Fed [463]

Work= force x displacement :)

8 0

2 years ago

A small meteorite with mass of 1 g strikes the outer wall of a communication satellite with a speed of 2Okm/s (relative to the s

strojnjashka [21]

Answer:

The energy coverted to heat is 200 kilojoules.

Explanation:

GIven the absence of external forces exerted both on the small meteorite and on the communication satellite, the Principle of Linear Momentum is considered and let suppose that collision is completely inelastic and that satellite is initially at rest. Hence, the expression for the satellite-meteorite system:

$m_{M}\cdot v_{M} + m_{S}\cdot v_{S} = (m_{M}+m_{S})\cdot v$

Where:

$m_{M}$ , $m_{S}$ - Masses of the small meteorite and the communication satellite, measured in kilograms.

$v_{M}$ , $v_{S}$ - Speeds of the small meteorite and the communication satellite, measured in meters per second.

$v$ - Final speed of the satellite-meteorite system, measured in meters per second.

The final speed of the satellite-meteorite system is cleared:

$v = \frac{m_{M}\cdot v_{M}+m_{S}\cdot v_{S}}{m_{M}+m_{S}}$

If $m_{M} = 1\times 10^{-3}\,kg$ , $m_{S} = 200\,kg$ , $v_{M} = 20000\,\frac{m}{s}$ and $v_{S} = 0\,\frac{m}{s}$ , the final speed is now calculated:

$v = \frac{(1\times 10^{-3}\,kg)\cdot \left(20000\,\frac{m}{s} \right)+(200\,kg)\cdot \left(0\,\frac{m}{s} \right)}{1\times 10^{-3}\,kg+200\,kg}$

$v = 0.1\,\frac{m}{s}$

Which means that the new system remains stationary and all mechanical energy from meteorite is dissipated in the form of heat. According to the Principle of Energy Conservation and the Work-Energy Theorem, the change in the kinetic energy is equal to the dissipated energy in the form of heat:

$K_{S} + K_{M} - K - Q_{disp} = 0$

$Q_{disp} = K_{S}+K_{M}-K$

Where:

$K_{S}$ , $K_{M}$ - Initial translational kinetic energies of the communication satellite and small meteorite, measured in joules.

$K$ - Kinetic energy of the satellite-meteorite system, measured in joules.

$Q_{disp}$ - Dissipated heat, measured in joules.

The previous expression is expanded by using the definition for the translational kinetic energy:

$Q_{disp} = \frac{1}{2}\cdot [m_{M}\cdot v_{M}^{2}+m_{S}\cdot v_{S}^{2}-(m_{M}+m_{S})\cdot v^{2}]$

Given that $m_{M} = 1\times 10^{-3}\,kg$ , $m_{S} = 200\,kg$ , $v_{M} = 20000\,\frac{m}{s}$ , $v_{S} = 0\,\frac{m}{s}$ and $v = 0.1\,\frac{m}{s}$ , the dissipated heat is:

$Q_{disp} = \frac{1}{2}\cdot \left[(1\times 10^{-3}\,kg)\cdot \left(20000\,\frac{m}{s} \right)^{2}+(200\,kg)\cdot \left(0\,\frac{m}{s} \right)^{2}-(200.001\,kg)\cdot \left(0.001\,\frac{m}{s} \right)^{2}\right]$ $Q_{disp} = 200000\,J$

$Q_{disp} = 200\,kJ$

The energy coverted to heat is 200 kilojoules.

4 0

3 years ago

Which theory states that if you are forced to smile at an event, you will enjoy it? A. The Schachter-Singer theory B. The Lazaru

Ronch [10]

Answer:

C. The facial feedback theory

Explanation:

The facial feedback theory as postulated by William James and connects back to the famous Charles Darwin talks about how facial expressions stimulate our emotional state of being. Based on this theory, the emotional experiences we have are determined by the looks on our faces.

According to the question, smiling at an event makes you enjoy it is an example of what the The facial feedback theory is explaining. Furthermore, smiling, which is a facial expression causes or stimulates an emotional state of enjoyment in that event.

7 0

3 years ago

A scientist carries out an experiment. How could she help other scientists judge the validity of her results?

NNADVOKAT [17]

One way to do it is she could right down the data that she got

4 0

3 years ago

Read 2 more answers