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4 years ago

7

A kayaker needs to paddle north across a 100 -m wideharbor. The tide is going out, creating a tidal current that flowsto the eas

t at 2.0 m/s. The Kayaker can paddle with a speed of3.0m/s.
a. In which direction shoule he paddle in order to travel straightacross the harbor ?
b. How long will it take him to cross ?

A body diagram and step by step precise solution willgive me a better understanding .. thanks for you help..

1 answer:

KATRIN_1 [288]4 years ago

8 0

Answer:

a) v_Nort = 2.236 m / s

, θ = 56.3º, b) t= 53.76 s

Explanation:

This exercise should use the addition of vectors, we have a kayak speed of v₁ = 3 m / s and an eastward speed of water v₂ = 2.0 m / s.

They ask us to cross the river that is to the north, we see that the speed of the kayak is the hypotenuse of the triangula, see attached

v₁² = v_nort² + v₂²

v _nort² = v₁² –v₂²

v_nort = √ (3² - 2²)

v_Nort = 2.236 m / s

For the angle we can use trigonometry

tan θ = v₂ / v₁

θ = tan⁻¹ v₂ / v₁

θ = tan⁻¹ 2/3

θ = 33.7º

This angle measured from the positive side of the x axis is

θ = 90 - 33.7

θ = 56.3º

b) we look for the northward component of this speed

sin 56.3 = $v_{y}$ / v_nort

v_{y} = v_nort sin 56.3

v_{y} = 2.236 sin 56.3

v_{y} = 1.86 m/s

The time is

v_{y} = y/t

t = y/v_{y}

t =100/ 1.86

t= 53.76 s

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3 years ago

A plane has a mass of 360,000 kg takes-off at a speed of 300 km/hr. i) What should be the minimum acceleration to take off if th

melomori [17]

Answer:

i) the minimum acceleration to take off is 22500 km/h²

ii) the required time needed by the plane from starting to takeoff is 0.0133 hrs

iii) required force that the engine must exert to attain acceleration is 625 kN

Explanation:

Given the data in the question;

mass of plane m = 360,000 kg

take of speed v = 300 km/hr = 83.33 m/s

i)

What should be the minimum acceleration to take off if the length of the runway is 2.00 km

from Newton's equation of motion;

v² = u² + 2as

we know that a plane starts from rest, so; u = 0

given that distance S = 2 km

we substitute

(300)² = 0² + ( 2 × a × 2 )

90000 = 4 × a

a = 90000 / 4

a = 22500 km/h²

Therefore, the minimum acceleration to take off is 22500 km/h²

ii) At this acceleration, how much time would the plane need from starting to takeoff.

from Newton's equation of motion;

v = u + at

we substitute

300 = 0 + 22500 × t

t = 300 / 22500

t = 0.0133 hrs

Therefore, the required time needed by the plane from starting to takeoff is 0.0133 hrs

iii) What force must the engines exert to attain this acceleration

we know that;

F = ma

acceleration a = 22500 km/hr² = 1.736 m/s²

so we substitute

F = 360,000 kg × 1.736 m/s²

F = 624960 N

F = 625 kN

Therefore, required force that the engine must exert to attain acceleration is 625 kN

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3 years ago

How much energy is contained in the mass of a 60-kilogram person?

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3 years ago

Read 2 more answers

How did newtons investigation of light followe one form of the scientific method

IrinaVladis [17]

Briefly the Scientific Method (i.e. hypothesis-driven research) involves Observation, Hypothesis, Controlled Experiment and Conclusion. More specifically:

Initial Observations:

You notice something, and wonder why it happens. You see something and wonder what causes it. You want to know how or why something works. You ask questions about what you have observed. You want to investigate. The first step is to clearly write down exactly what you have observed.

Information Gathering:

Find out about what you want to investigate. Read books, magazines or ask professionals to learn about the effect or area of study. Keep track of where you got your information from.

Title the Project:

Choose a title that describes the effect or thing you are investigating. The title should be short and summarize what the investigation will deal with.

State the Purpose of the Project

What do you want to find out? Write a statement that describes what you want to do. Use your observations and questions to write the statement.

Identify Variables:

Based on your gathered information, make an educated guess about what types of things affect the system you are working with. Identifying variables is necessary before you can make a hypothesis.

Make Hypothesis:

When you think you know what variables may be involved, think about ways to change one at a time. If you change more than one at a time, you will not know what variable is causing your observation. Sometimes variables are linked and work together to cause something. At first, try to choose variables that you think act independently of each other. At this point, you are ready to translate your questions into hypothesis. A hypothesis is a question which has been reworded into a form that can be tested by an experiment.

Make a list of your answers to the questions you have. This can be a list of statements describing how or why you think the observed things work. These questions must be framed in terms of the variables you have identified. There is usually one hypothesis for each question you have. You must do at least one experiment to test each hypothesis. This is a very important step.

Design Experiments to Test Your Hypothesis

Design an experiment to test each hypothesis. Make a step-by-step list of what you will do to answer each question. This list is called an experimental procedure or specific aims.

Perform Experiments and Record Observations

Summarize Results

Summarize what happened. This can be in the form of a table of processed numerical data, or graphs. It could also be a written statement of what occurred during experiments. It is from calculations using recorded data that tables and graphs are made. Studying tables and graphs, we can see trends that tell us how different variables cause our observations. Based on these trends, we can draw conclusions about the system under study. These conclusions help us confirm or deny our original hypothesis.

Draw Conclusions

Using the trends in your experimental data and your experimental observations, try to answer your original questions. Is your hypothesis correct? Now is the time to pull together what happened, and assess the experiments you did. Other things you can mention in the conclusion

If your hypothesis is not correct, what could be the answer to your question?

Summarize any difficulties or problems you had doing the experiment.

Do you need to change the procedure and repeat your experiment?

What would you do different next time?

List other things you learned

6 0

3 years ago

Three people pull simultaneously on a stubborn donkey. Jack pulls directly ahead of the donkey with a force of 64.7 N64.7 N , Ji

WARRIOR [948]

Answer:

(a) Magnitude of force is 262.51 N

(b) Angle with East direction is $-14.75^{o}$

Explanation:

Force by Jack in vector form

$\overrightarrow F _1} = 64.7{\rm{ N}}\left( {\hat i} \right)$

Force by Jill in Vector form is given by

$\begin{array}{c}\\{\overrightarrow F _2} = 86.5{\rm{ N }}\cos {\rm{4}}{{\rm{5}}^{\rm{o}}}\left( {\hat i} \right) + 86.5{\rm{ N }}\sin {\rm{4}}{{\rm{5}}^{\rm{o}}}\left( {\widehat j} \right)\\\\ = 61.16{\rm{ N}}\left( {\hat i} \right) + 61.16{\rm{ N}}\left( {\widehat j} \right)\\\end{array}$

Force by Jane is

$\begin{array}{c}\\{\overrightarrow F _3} = 181{\rm{ N }}\cos {\rm{4}}{{\rm{5}}^{\rm{o}}}\left( {\hat i} \right) + 181{\rm{ N }}\sin {\rm{4}}{{\rm{5}}^{\rm{o}}}\left( { - \widehat j} \right)\\\\ = 128{\rm{ N}}\left( {\hat i} \right) + 128{\rm{ N}}\left( { - \widehat j} \right)\\\end{array}$

Net force is:

$\overrightarrow F = {\overrightarrow F _1} + {\overrightarrow F _2} + {\overrightarrow F _3}$

Hence

$\begin{array}{c}\\\overrightarrow F = 64.7{\rm{ N}}\left( {\hat i} \right) + 61.16{\rm{ N}}\left( {\hat i} \right) + 61.16{\rm{ N}}\left( {\widehat j} \right) + 128{\rm{ N}}\left( {\hat i} \right) + 128{\rm{ N}}\left( { - \widehat j} \right)\\\\ = 253.86{\rm{ N}}\left( {\hat i} \right) - 66.84{\rm{ N}}\left( {\widehat j} \right)\\\end{array}$

The net force will be given by

$F = \sqrt {{{\left( {{F_x}} \right)}^2} + {{\left( {{F_y}} \right)}^2}$

Since $F_{x}=253.86N$ and $F_{y}=-66.84N$

$\begin{array}{c}\\F = \sqrt {{{\left( {253.86{\rm{ N}}} \right)}^2} + {{\left( { - 66.84{\rm{ N}}} \right)}^2}} \\\\ = {\bf{262.51 N}}\\\end{array}$

The direction of net force is:

$\theta = {\tan ^{ - 1}}\left {\frac{{{F_y}}}{{{F_x}}}}$

Since $F_{x}=253.86N$ and $F_{y}=-66.84N$

$\begin{array}{c}\\\theta = {\tan ^{ - 1}}\left( {\frac{{ - 66.84{\rm{ N}}}}{{253.86{\rm{ N}}}}} \right)\\\\ = {\tan ^{ - 1}}\left( { - 0.2633} \right)\\\\ = {\bf{ - 14}}{\bf{.7}}{{\bf{5}}^{\bf{o}}}\\\end{array}$

The angle with East direction is $-14.75^{o}$

Net force exerted on the donkey is in the south-east direction. So, the angle of net force from the east direction is $-14.75^{o}$ and it is $14.75^{o}$ from the south.

5 0

3 years ago