6) The length of year is equal to the time it takes for one *

A river flows due east at 1.60 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant v

Citrus2011 [14]

Answer:

part (a) $v\ =\ 10.42\ at\ 81.17^o$ towards north east direction.

part (b) s = 46.60 m

Explanation:

Given,

velocity of the river due to east = $v_r\ =\ 1.60\ m/s.$
velocity of the boat due to the north = $v_b\ =\ 10.3\ m/s.$

part (a)

River is flowing due to east and the boat is moving in the north, therefore both the velocities are perpendicular to each other and,

Hence the resultant velocity i,e, the velocity of the boat relative to the shore is in the North east direction. velocities are the vector quantities, Hence the resultant velocity is the vector addition of these two velocities and the angle between both the velocities are $90^o$

Let 'v' be the velocity of the boat relative to the shore.

$\therefore v\ =\ \sqrt{v_r^2\ +\ v_b^2}\\\Rightarrow v\ =\ \sqrt{1.60^2\ +\ 10.3^2}\\\Rightarrow v\ =\ 10.42\ m/s.$

Let $\theta$ be the angle of the velocity of the boat relative to the shore with the horizontal axis.

Direction of the velocity of the boat relative to the shore. $\therefore Tan\theta\ =\ \dfrac{v_b}{v_r}\\\Rightarrow Tan\theta\ =\ \dfrac{10.3}{1.60}\\\Rightarrow \theta\ =\ Tan^{-1}\left (\dfrac{10.3}{1.60}\ \right )\\\Rightarrow \theta\ =\ 81.17^o$

part (b)

Width of the shore = w = 300m

total distance traveled in the north direction by the boat is equal to the product of the velocity of the boat in north direction and total time taken

Let 't' be the total time taken by the boat to cross the width of the river. $\therefore w\ =\ v_bt\\\Rightarrow t\ =\ \dfrac{w}{v_b}\\\Rightarrow t\ =\ \dfrac{300}{10.3}\\\Rightarrow t\ =\ 29.12 s$

Therefore the total distance traveled in the direction of downstream by the boat is equal to the product of the total time taken and the velocity of the river $\therefore s\ =\ u_rt\\\Rightarrow s\ =\ 1.60\times 29.12\\\Rightarrow s\ =\ 46.60\ m$

7 0

3 years ago

Energy is the ability to do work. True or false

Blababa [14]

Work can be defined as the energy transferred from a body to its sorroundings, the energy spent to move a body, or the energy you need to alter a charged particle, so no energy, no work; thus, the statement is true.

4 0

2 years ago

A cylindrical container closed of both end has a radius of 7cm and height of 6cm A.)find the total surface area of the container

Natalka [10]

Given:

A cylindrical container closed of both end has a radius of 7cm and height of 6cm.

Explanation:

A.) Find the total surface area of the container.

A = 2πrh + 2πr²
A = 2(3.14)(7)(6) + 2(3.14)(7 × 7)
A = 263.76 + 307.72
A = 571.48

B.) Find the volume of the container.

V = πr²h
V = (3.14)(7×7)(6)
V = 923.16

Not sure huhuness.

#CarryOnLearning

8 0

3 years ago

Read 2 more answers

What is the acceleration of a 600,000 kg freight train, if each of itsthree engines can provide 100,000 n of force?

sergey [27]

The acceleration of a 600,000 kg freight train, if each of its three engines can provide 100,000N of force is 0.167m/s².

<h3>How to calculate acceleration?</h3>

The acceleration of a freight train can be calculated using the following formula:

Force = mass × acceleration

According to this question, a 600,000kg freight train can produce 100,000N of force. The acceleration is as follows:

100,000 = 600,000 × a

100,000 = 600,000a

a = 0.167m/s²

Therefore, the acceleration of a 600,000 kg freight train, if each of its three engines can provide 100,000N of force is 0.167m/s².

Learn more about acceleration at: brainly.com/question/12550364

#SPJ1

6 0

1 year ago

Select the correct answer.

anyanavicka [17]

<h2>MULTIPLE CHOICES</h2>

$\large\mathcal{QUESTION:}$

What is the basic unit of all matter?

$\large\mathcal{CHOICES:}$

OA neutron
OB. atom
OC. electron
OD. proton
OE. nucleus

$\large\mathcal{ANSWER:}$

B. Atom

_____

<u>Atom</u> is the smallest, <u>indivisible unit of a chemical</u> <u>element and the fundamental unit of matter</u>. It consists of a nucleus (neutrons + protons) surrounded by an electron cloud. The <u>atom</u> is the smallest unit of matter that cannot be divided chemically and is a building block with its own set of properties.

<h3>#ProvideUniqueAnswers</h3>

6 0

2 years ago