1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Bingel [31]
3 years ago
6

A bird flies in the xy-plane with a velocity vector givenby v = (α-βt2)i + γtj with α=2.4m/s,β=1.6m/s3 and γ=4m/s2 . Thepositive

y-direction is vertically upward. At t=0 the birdis at the origin.
1. Calculate the position vector of the bird as a function oftime.
2. Calculate the acceleration vector of the bird as a function oftime.
3. What is the bird's altitude (y-coordinate) as it fliesover x=0 for the first time after t=0.
Physics
1 answer:
Finger [1]3 years ago
4 0

Answer:

1. r(t) = (\alpha t - \frac{\beta t^3}{3})\^i + (\frac{\gamma t^2}{2})\^j

2. a(t) = \frac{dv(t)}{dt} = -2\beta t \^i + \gamma \^j

3. r(t=2.12) = (6~{\rm m})\^j

Explanation:

The velocity vector is

v(t) = (\alpha - \beta t^2)\^i + (\gamma t)\^j

1. The position vector can be found by integrating the velocity vector.

r(t) = \int v(t) dt = (\alpha t - \frac{\beta t^3}{3} + C_1)\^i + (\frac{\gamma t^2}{2} + C_2)\^j

At t = 0, the bird is at the origin, so the integration constants can be determined.

r(0) = C_1 \^i + C_2 \^y = 0

Therefore, C1 and C2 are equal to zero.

r(t) = (\alpha t - \frac{\beta t^3}{3})\^i + (\frac{\gamma t^2}{2})\^j

2. The acceleration vector is the derivative of the velocity vector with respect to time.

a(t) = \frac{dv(t)}{dt} = -2\beta t \^i + \gamma \^j

3. We will first find the time when the x-component of the position vector is equal to zero.

\alpha t - \frac{\beta t^3}{3} = 0\\\alpha = \frac{\beta t^2}{3}\\t = \sqrt{\frac{3\alpha}{\beta}} = 2.12~s

We will plug in this value into the y-component of the position vector.

y(t) = \frac{\gamma t^2}{2}\\y(2.12) = \frac{4(2.12)^2}{2} = 9~m

You might be interested in
Consider an electron that is 10-10 m from an alpha particle (9 = 3.2 x 10-19 C). (Enter the magnitudes.) (a) What is the electri
Studentka2010 [4]

Answer:

a)E=2.88*10^{11}N/C

b)E=1.44*10^{11}N/C

c)F=4.61*10^{-8}N

Explanation:

We use the definition of a electric field produced by a point charge:

E=k*q/r^2

<u>a)Electric Field  due to the alpha particle:</u>

E=k*q_{alpha}/r^2=9*10^9*3.2*10^{-19}/(10^{-10})^2=2.88*10^{11}N/C

<u>b)Electric Field  due to electron:</u>

E=k*q_{electron}/r^2=9*10^9*1.6*10^{-19}/(10^{-10})^2=1.44*10^{11}N/C

<u>c)Electric Force on the alpha particle, on the electron:</u>

The alpha particle and electron feel the same force but with opposite direction:

F=k*q_{electron}*q_{alpha}/r^2=9*10^9*1.6*10^{-19}*3.2*10^{-19}/(10^{-10})^2=4.61*10^{-8}N

4 0
3 years ago
Several wires of varying thickness are all made of the same material and all have the same length. If the wires are arranged in
aev [14]

Answer:

Option A is correct.

The wires will be arranged in order of increasing resistance.

Explanation:

The resistance of a wire is given by

r = (ρl)/A

where r = resistance of the wire

ρ = resistivity of the wire

L = length of the wire

A = cross sectional area of the wire

Provided all the other parameters are constant, resistance is inversely proportional to cross sectional area

r ∝ (1/A)

And the the cross sectional Area of the wire increases with increase in thickness & decreases with thickness

So, decreasing thickness ----> Decreasing Cross sectional Area ----> Increasing resistance.

5 0
3 years ago
An electric dipole is formed from ±1.00nC charges spaced 3.00 mm apart. The dipole is at the origin, oriented along the x-axis.
Ronch [10]

Answer:

Value of electric field along the axis and equitorial axis  E=31.25\ N/c and E = 15.625\ N/c respectively.

Explanation:

Given :

Distance between charges , d = 3 \ mm =\dfrac{3}{1000}\ m=3\times 10^{-3}\ m.

Magnitude of charges , q=1\ nC = 10^{-9}\ C.

Dipole moment , p=qL=10^{-9}\times 3\times 10^{-3}=3\times 10^{-12} \ C\ m.

Case A) (x,y) = (12.0 cm, 0 cm) :

Electric field of dipole in its axis ,

E=\dfrac{2kp}{r^3}

Putting all values and r=12\times 10^{-2}\ m.

We get , E=31.25\ N/c.

Case B) (x,y) = (0 cm, 12.0 cm) :

Electric field of dipole on equitorial axis ,

E = \dfrac{kp}{r^3}

Putting all values and r=12\times 10^{-2}\ m.

We get , E = 15.625\ N/c.

Hence , this is the required solution.

7 0
3 years ago
Earth’s polar ice caps contain about 2.3 × 1019 kg of ice. This mass contributes essentially nothing to the moment of inertia of
sp2606 [1]

Answer:

Explanation:

Initial moment of inertia of the earth I₁ = 2/5 MR² , M is mss of the earth and R is the radius . If ice melts , it forms an equivalent shell of mass  2.3 x 10¹⁹ Kg

Final moment of inertia I₂ = 2/5 M R² + 2/3  x 2.3 x 10¹⁹ x R²

For change in period of rotation we shall apply conservation of angular momentum law

I₁ ω₁  = I₂ ω₂  ,  ω₁ and   ω₂ are angular velocities initially and finally .

I₁ / I₂     =  ω₂ / ω₁

I₁ / I₂     =  T₁ / T₂  , T₁ , T₂ are time period initially and finally .

T₂ / T₁ = I₂ / I₁

(2/5 M R² + 2/3  x 2.3 x 10¹⁹ x R²) / 2/5 MR²

1 + 5 / 3  x 2.3 x 10¹⁹ / M

= 1 + 5 / 3  x 2.3 x 10¹⁹ / 5.97 x 10²⁴

= 1 + .0000064

T₂ = 24 (1 + .0000064)

= 24 hours + .55 s

change in length of the day = .55 s .

3 0
3 years ago
2. Xét một điểm nằm trên vành ngoài của lốp xe máy cách trục bánh xe môtô 25cm.
Rashid [163]

Answer:

b. Cho biết tốc độ của xe là 4m/s. Hãy tính tốc độ góc của điểm trên vành ngoài bánh xe.

Explanation:

#CarryOnLearning

6 0
2 years ago
Other questions:
  • The discovery of Uranus________.
    7·2 answers
  • A roller coaster track is a good example of the law of conservation of energy. Use this law to explain these facts about a rolle
    12·2 answers
  • Calculate the electric field at the center of a square 46.4 cm on a side, if one corner is occupied by a +42.0 µc charge and the
    11·1 answer
  • A 30 N block is being pulled along a horizontal surface with an acceleration of 6 m/s2 by a rope. The coefficient of kinetic fri
    13·1 answer
  • Las ovejas son animales sociales que seguirán a la oveja guía a cualquier lugar que decida ir. Pensando en esto, describa un mom
    9·1 answer
  • A 0.50-T magnetic field is directed perpendicular to the plane of a circular loop of radius 0.25 m. What is the magnitude of the
    5·1 answer
  • Jasmine leaves her house to go for a run. She isn't paying attention to where
    12·1 answer
  • Determine the density of a liquid from the following data .
    13·2 answers
  • A meter stick is found to balance at the 49.7-cm mark when placed on a fulcrum. When a 65.5-gram mass is attached at the 21.0-cm
    13·1 answer
  • Gravity can *
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!