Prove : cos(3x)=sin(2x)

John drives a distance of 90 Km to the right at a steady speed of V1=25.00 m/s. Then he stops at the gas station for 10 minutes.

aleksley [76]

a. Speed is defined as rate of change of distance per unit time whereas velocity is defined as rate of change of displacement per unit time.

b. $t=6000\ s$ is the total time taken in the trip

c. $d=126000\ m$ is the total distance

d. $s=54000\ m$ towards right from the starting point.

e. $v_a=21\ m.s^{-1}$

f. $\vec v_a=9\ m.s^{-1}$ towards right.

Explanation:

a.

Speed is a scalar quantity while velocity is a vector quantity.

Speed is defined as rate of change of distance per unit time whereas velocity is defined as rate of change of displacement per unit time.

Speed is a directionless quantity while velocity constitutes direction.

b.

Total time of round trip when we're given:

distance travelled to the right, $d_r=90000\ m$

speed while travelling to the right, $v_r=25\ m.s^{-1}$

time spent at gas station, $t_g=600\ s$

time spent while travelling back towards the left, $t_l=30\times 60=1800\ s$

speed while travelling to the left, $v_{_l}=20\ m.s^{-1}$

Now time taken for travelling towards right:

$t_r=\frac{d_r}{v_r}$

$t_r=\frac{90000}{25}$

$t_r=3600\ s$

Therefore total time taken in the round trip:

$t=t_r+t_l+t_g$

$t=3600+600+1800$

$t=6000\ s$

c.

Now, distance travelled towards left:

$d_l=v_{_l}\times t_l$

$d_l=20\times1800$

$d_l=36000\ m$

Therefore total distance:

$d=d_l+d_r$

$d=36000+90000$

$d=126000\ m$

d.

Now, total displacement:

$s=d_r-d_l$

$s=90000-36000$

$s=54000\ m$ towards right from the starting point.

e.

Average speed:

$v_a=\frac{d}{t}$

$v_a=\frac{126000}{6000}$

$v_a=21\ m.s^{-1}$

f.

Average velocity:

$\vec v_a=\frac{s}{t}$

$\vec v_a=\frac{54000}{6000}$

$\vec v_a=9\ m.s^{-1}$ towards right.

4 0

2 years ago

The ends of a bar magnet are called _____. poles domains fields currents

Leto [7]

1.

The ends of a bar magnet are called poles. It has a north pole and a south pole. To magnet two things, the poles must be linked oppositely. North to south and south to north.

3 0

2 years ago

Read 2 more answers

A cylindrical diving bell is open at the bottom and closed at the top, and is 5m tall. The bell is open to atmospheric air until

laila [671]

Answer:

a) y = 0.35 m, b) hydrostatic balance

Explanation:

a) For this fluid mechanics exercise, let's use that the pressure at a given level is the same, let's set a level on the bell shape.

The pressure inside is

P_interior = P₀ + ρ g h ’

The pressure outside

P_exterior = Pₐ + ρ g h

as the point is at the same level the pressures are equal

P_interior = P_exterior

P₀ + ρ g h ’= Pₐ + ρ g h

h ’= (Pₐ- P₀) + ρ g h

To calculate P₀ they indicate that the pressure increases 10⁵ Pa for every 10 m, we use a direct rule of proportions or rule of three

P₀ = 10⁵ (40 + h ’) / 10 = 4 10⁵ + h’ 10⁴

the positive sign is because the water inside the hood also increases the air pressure.

we substitute

(4 10⁵ + h’ 10⁴) + ρ g h’ = Pₐ + ρ g h

h’ (ρ g + 10⁴) = Pₐ - 4 10⁵ + ρ h h

h’ (1000 9.8 + 10⁴) = (1 10⁵ -4 10⁵) + 1000 9.8 40

h' (1.98 10⁴) = -3 105 + 3.92 10⁵

h’ = $- \frac{0.92 \ 10^5 }{1.98 \ 10^4 }$

h ’= -4.65 m

as the hood is only 5 m high, the free air space is

Y = 5 - 4.65

y = 0.35 m

it is very little free space

B) The pressure outside and inside the hood is the same, the water rises inside the hood until the pressures equalize and at this point the force is equal and in the opposite direction, which is why the system is in hydrostatic balance.

4 0

2 years ago

How did the distance from the sun affect the creation of planets?

cestrela7 [59]

The closest planet from the Sun is Mercury and the furthest is Pluto ( called the Dwarf Planet ). The 4 planets closest to the Sun ( Mercury, Venus, Earth, Mars ) are the inner planets, made up mainly of rock and much denser than the 4 outer planets. The outer planets are called the Gas giants ( Jupiter, Saturn, Uranus and Neptune ). They are made up mostly of gasses with smaller solid and liquid centers. The planets are created in a cloud of gas and dust ( a Solar nebula ). The center of the cloud became a star - the Sun. Closer to the center could stand only rocky material ( the inner planets ) and in the outer regions was icy material that creates the Gas giants.Because of it`s position in the Solar nebula, the proto-Jupiter became the biggest of the planets. From the Jupiter the planets became massive. Those formed closer to the proto-Sun were smaller and rocky.

6 0

2 years ago

Read 2 more answers

If the earth rock takes 2.00 s to reach its highest point, how long will it take the moon rock to do so

spin [16.1K]

12.0 s

Explanation:

First, let's find the initial vertical velocity of the rock on earth. We know that

vy = v0y - gt

where g = 9.8 m/s^2. When the rock reaches its highest point, vy = 0. So if it takes 2.00 s to reach the maximum height, the initial velocity of the rock is

v0y = (9.8 m/s^2)(2.00 s) = 19.6 m/s.

We know that the moon only has 1/6 of earth's gravity. Therefore, if the same rock is given the same vertical velocity as on earth, then the time it takes to reach its maximum height is

voy = gt ---> t = voy/g

t = (19.6 m/s)/(9.8/6 m/s^2)

= 12.0 s

8 0

2 years ago

Prove : cos(3x)=sin(2x)​

Prove : cos(3x)=sin(2x)