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Ira Lisetskai [31]

2 years ago

13

Suppose a police officer is 1/2 mile south of an intersection, driving north towards the intersection at 30 mph. at the same tim

e, another car is 1/2 mile east of the intersection, driving east (away from the intersection) at an unknown speed. the officer's radar gun indicates 15 mph when pointed at the other car (that is, the straight-line distance between the officer and the other car is increasing at a rate of 15 mph). what is the speed of the other car?

2 answers:

IgorLugansk [536]2 years ago

6 0

Answer:

$v = 51.2 mph$

Explanation:

Velocity of police car

$v_p = 30 mph$ towards North

velocity of the car with respect to police car

$v_{cp} = 15 mph$

Speed of the other car is given with respect to police car so let say the speed of other car is "v"

Now the component of this speed along the line joining two cars is

$v_1 = v cos45$

similarly speed of police car along the line joining two cars is given as

$v_2 = v sin45$

now we can find the relative speed

$v_{12} = v_1 - v_2$

$15 mph = vcos45 - 30cos45$

$v = 51.2 mph$

aleksandr82 [10.1K]2 years ago

3 0

In triangle ABC , using Pythagorean theorem

BC = sqrt(AB² + AC²)

r = sqrt(y² + x²) eq-1

taking derivative both side relative to "t"

dr/dt = (1/(2 sqrt(y² + x²) ) ) (2 y (dy/dt) + 2 x (dx/dt))

dr/dt = (1/(2 sqrt(0.5² + 0.5²) ) ) (2 (0.5) (dy/dt) + 2 (0.5) (dx/dt))

dr/dt = (1/(2 sqrt(0.5² + 0.5²) ) ) ( v₁ + v₂)

15= (1/(2 sqrt(0.5² + 0.5²) ) ) ( - 30 + v₂)

v₂ = 51.2 m/s

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A charge of uniform volume density (40 nC/m3) fills a cube with 8.0-cm edges. What is the total electric flux through the surfac

GREYUIT [131]

Answer:

The flux through the surface of the cube is $2.314\ Nm^{2}/C$

Solution:

As per the question:

Edge of the cube, a = 8.0 cm = $8.0\times 10^{- 2}\ m$

Volume Charge density, $\rho_{v} = 40 nC/m^{3} = 40\times {- 9}\ C/m^{3}$

Now,

To calculate the electric flux:

$\phi = \frac{q}{\epsilon_{o}}$ (1)

where

$\phi$ = electric flux

$\epsilon_{o} = 8.85\times 10^{- 12}\ F/m$ = permittivity of free space

Volume Charge density for the given case is given by the formula:

$\rho_{v} = \frac{Total\ charge, q}{Volume of cube, V}$ (2)

Volume of cube, $V = a^{3}$

Thus

$V = (8.0\times 10^{- 2})^{3} = 5.12\times 10^{- 4}\ m^{3}$

Thus from eqn (2), the total charge is given by:

$q = \rho_{v}V = 40\times {- 9}\times 5.12\times 10^{- 4}$

$q = 2.048\times 10^{-11}\ F = 20.48\ pF$

Now, substitute the value of 'q' in eqn (1):

$\phi = \frac{2.048\times 10^{-11}}{8.85\times 10^{- 12}} = 2.314\ Nm^{2}/C$

5 0

2 years ago

A 4.50-kg wheel that is 34.5 cm in diameter rotates through an angle of 13.8 rad as it slows down uniformly from 22.0 rad/s to 1

Mila [183]

Answer:

-10.9 rad/s²

Explanation:

ω² = ω₀² + 2α(θ - θ₀)

Given:

ω = 13.5 rad/s

ω₀ = 22.0 rad/s

θ - θ₀ = 13.8 rad

(13.5)² = (22.0)² + 2α (13.8)

α = -10.9 rad/s²

6 0

2 years ago

Read 2 more answers

A jetboat is drifting with a speed of 5.0\,\dfrac{\text m}{\text s}5.0 s m 5, point, 0, start fraction, start text, m, end tex

love history [14]

The question is incomplete. Here is the entire question.

A jetboat is drifting with a speed of 5.0m/s when the driver turns on the motor. The motor runs for 6.0s causing a constant leftward acceleration of magnitude 4.0m/s². What is the displacement of the boat over the 6.0 seconds time interval?

Answer: Δx = - 42m

Explanation: The jetboat is moving with an acceleration during the time interval, so it is a <u>linear</u> <u>motion</u> <u>with</u> <u>constant</u> <u>acceleration</u>.

For this "type" of motion, displacement (Δx) can be determined by:

$\Delta x = v_{i}.t + \frac{a}{2}.t^{2}$

$v_{i}$ is the initial velocity

a is acceleration and can be positive or negative, according to the referential.

For Referential, let's assume rightward is positive.

Calculating displacement:

$\Delta x = 5(6) - \frac{4}{2}.6^{2}$

$\Delta x = 30 - 2.36$

$\Delta x$ = - 42

Displacement of the boat for t=6.0s interval is $\Delta x$ = - 42m, i.e., 42 m to the left.

8 0

2 years ago

What are the two forces that keep a pendulum swinging?

NemiM [27]

The correct answer would be the third option. The two forces that keep a pendulum swinging would be tension and gravity. The force of gravity causes the pendulum to keep it swinging and tension blocks all resistances in order for the motion to continue.

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2 years ago

What is the de Broglie wavelength of a bullet of mass 0.075 kg traveling at 350 m/s? Planck's Constant is 6.63 × 10−34 J⋅s.

jasenka [17]

Answer:

De Broglie wavelength of the bullet is given as

$\lambda = 2.5 \times 10^{-35} m$

Explanation:

As per De Broglie hypothesis we know that the wavelength of De Broglie waves is the ratio of Plank's constant and momentum of the particle

here we know that the bullet mass is

m = 0.075 kg

speed of the bullet is given as

v = 350 m/s

Now we have

$P = (0.075)(350)$

$P = 26.25 kg m/s$

Now we know that

$\lambda = \frac{h}{P}$

$\lambda = \frac{6.63 \times 10^{-34}}{26.25}$

$\lambda = 2.5 \times 10^{-35} m$

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2 years ago