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2 years ago

An object is moving in the plane according to these parametric equations:

Physics

2 answers:

morpeh [17]2 years ago

8 0

Answer:

.a vx = -3π

b.vy = 0

c.c. m = sin(4πt + π/2) / [πt + cos(4πt + π/2)]

d.m = sin(4π/6 + π/2) / [π/6 + cos(4π/6 + π/2)]

e. t = -1.0

f.f. t = -0.35

g.vx = π - 4πsin (4π(0.124) + π/2)

h.vmax=4π cos (4π(0.045) + π/2)

i.s(t) = [x(t)^2 + y(t)^2]^(1/2)

s'(t) = d [x(t)^2 + y(t)^2]^(1/2) / dt

Explanation:

x(t) = πt + cos(4πt + π/2)

differentiating te orizontal distance wit respect to time t, will give horizontal velocity

change in displacement per change in time is velocity

vx = dx/dt = π - 4πsin (4πt + π/2)

vx = π - 4π sin (0 + π/2)

at t =0, substituting te value of t into the above

vx = π - 4π (1)

vx = -3π

y(t) = sin(4πt + π/2)

differentiate wit respect to t

dy/dt=4π cos (4πt + π/2)

π/2=90

when t=0

b. vy=dy/dt = 4π cos (4πt + π/2)

vy = 0

c. slope of te tanent line

y(t)/x(t)

c. m = sin(4πt + π/2) / [πt + cos(4πt + π/2)]

d. at t=1/6, we substitute into answer gotten in c

m = sin(4π/6 + π/2) / [π/6 + cos(4π/6 + π/2)]

e. t = -1.0

f. t = -0.35

g. Solve for t

vx = π - 4πsin (4πt + π/2) = 0

at maximum v=0

(4πt + π/2)=0.0043

t=-π/2+0.0043/(4π)

t=-0.124

vx = π - 4πsin (4π(0.124) + π/2)

h. Solve for t

vy = 4π cos (4πt + π/2) = 0

(4πt + π/2=1

t=0.57/4π

t=0.045

vmax=4π cos (4π(0.045) + π/2)

i. resultant of te displacement

s(t) = [x(t)^2 + y(t)^2]^(1/2)

h. s'(t) = d [x(t)^2 + y(t)^2]^(1/2) / dt

s'(t)=

k and l. Solve for the values of t

d [x(t)^2 + y(t)^2]^(1/2) / dt = 0

And substitute to determine the maximum and minimum speeds.

aniked [119]2 years ago

5 0

A. The horizontal velocity is
vx = dx/dt = π - 4πsin (4πt + π/2)
vx = π - 4π sin (0 + π/2)
vx = π - 4π (1)
vx = -3π

b. vy = 4π cos (4πt + π/2)
vy = 0

c. m = sin(4πt + π/2) / [<span>πt + cos(4πt + π/2)]

d. m = </span>sin(4π/6 + π/2) / [π/6 + cos(4π/6 + π/2)]

e. t = -1.0

f. t = -0.35

g. Solve for t
vx = π - 4πsin (4πt + π/2) = 0
Then substitute back to solve for vxmax

h. Solve for t
vy = 4π cos (4πt + π/2) = 0
The substitute back to solve for vymax

i. s(t) = [<span>x(t)^2 + y</span>(t)^2]^(1/2)

h. s'(t) = d [x(t)^2 + y(t)^2]^(1/2) / dt

k and l. Solve for the values of t
d [x(t)^2 + y(t)^2]^(1/2) / dt = 0
And substitute to determine the maximum and minimum speeds.

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lidiya [134]

Answer: 1 m/s

Explanation:

We have an object whose position $r$ is given by a vector, where the components X and Y are identified by the unit vectors $i$ and $j$ (where each unit vector is defined to have a magnitude of exactly one):

$r=[2 m + (2 m/s) t] i + [3 m - (1 m/s^{2})t^{2}] j$

On the other hand, velocity is defined as the variation of the position in time:

$V=\frac{dr}{dt}$

This means we have to derive $r$ :

$\frac{dr}{dt}=\frac{d}{dt}[2 m + (2 m/s) t] i + \frac{d}{dt}[3 m - (1 m/s^{2})t^{2}] j$

$\frac{dr}{dt}=(2 m/s) i - (\frac{1}{2} m/s^{2} t) j$ This is the velocity vector

And when $t=2s$ the velocity vector is:

$\frac{dr}{dt}=(2 m/s) i - (\frac{1}{2} m/s^{2} (2 s)) j$

$\frac{dr}{dt}=2 m/s i - 1m/s j$ This is the velocity vector at 2 seconds

However, the solution is not complete yet, we have to find the module of this velocity vector, which is the speed $S$ :

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Finally:

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2 years ago

A circular coil has a 10.0 cm radius and consists of 30.0 closely wound turns of wire. an externally produced magnetic field of

IrinaVladis [17]

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A = π(.1 m)^2
A = π/100 m^2

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The inductance on the coil given the current flows in a certain direction can be calculated by the product of the total number of turns in the coil and the flux of one loop over the current passing through. We do as follows:

L = N (ΦB ) / I
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2 years ago

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2 years ago

In a demonstration, a 4.00 cm2 square coil with 10 000 turns enters a larger square region with a uniform 1.50 T magnetic field

Kay [80]

Explanation:

It is given that,

Area of square coil, $A=4\ cm^2=0.0004\ m^2$

Side of the square, L = 0.02 m

Number of turns, N = 10000

Uniform magnetic field, B = 1.5 T

Speed, v = 100 m/s

An emf is induced in the coil which is given by :

$E=NBLv$

$E=10000\times 1.5\times 0.02\times 100$

E = 30000 V

Breakdown voltage of air, $V=4000\ V/cm=400000\ V/m$

Let d is the gap between the two wires connected to the ends of the coil and still get a spark. So,

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2 years ago

The superhero Green Lantern steps from the top of a tall building. He falls freely from rest to the ground, falling half the tot

ddd [48]

Answer:

1) its initial velocity is zero, 2) the downward direction as positive

3) h = 25.66 m

Explanation:

This is a free fall exercise.

1) with falls, its initial velocity is zero and the acceleration is constant throughout the path and is equal to the acceleration due to gravity.

2) a widely used selection to estimate the downward direction as positive

3) We know that for the second part of the fall

y₀ -y = h/2 at t = 1 s

y = y₀ + v₁ t + ½ g t²

where v₁ is the initial velocity of this interval at the point y = h / 2

v₁ t = (y -y₀) - ½ g t²

v₁ = h / 2 - ½ g t²

v₁ = h/2 - g/2

now let's write the equation for the first interval

v₁² = v₀² + 2 g (y₁ - y₀)

in this interval v₀ = 0

v₁² = 2 g (y₁ -y₀)

v₁² = 2g h/2

we write our system of equations

v₁² = (h/2 - g/2)²

v₁² = (2g h / 2)

(h /2 - g/2)² = (2g h / 2)

h² / 4 - 2 g/2 h/2 + (g/2)² = g h

h² / 4 - g h/2 - g h + g²/4 = 0

h² - 3 g h + g² =0

h² - 29.4 h +96.04 = 0

we solve the quadratic equation

h = [29.4 ±√ (29.4² - 4 96.04)] / 2

h = [29.4 ± 21.91] / 2

h₁ = 25.66 m

h₂ = 3.75 m

As the system takes more than 1 S to fall, the correct answer for the height is h = 25.66 m

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2 years ago