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denpristay [2]
3 years ago
6

Two particles are traveling through space. At time t the first particle is at the point (−1 + t, 4 − t, −1 + 2t) and the second

particle is at (−7 + 2t, −6 + 2t, −1 + t). (a) (5 Points) Do the paths of the two particles cross? If so, where?
Physics
1 answer:
Pie3 years ago
5 0

Answer:

Yes, the paths of the two particles cross.

Location of path intersection = ( 1 , 2 , 3)

Explanation:

In order to find the point of intersection, we need to set both locations equal to one another. It should be noted however, that the time for each particle can vary as we are finding the point where the <u>paths</u> meet, not the point where the particles meet themselves.

So, we can name the time of the first particle T_F ,  and the time of the second particle T_S.

Setting the locations equal, we get the following equations to solve for T_F and T_S:

(-1 + T_F) = (-7 + 2T_S)                     Equation 1

(4 - T_F) = (-6 + 2T_S)                        Equation 2

(-1 + 2T_F) = (-1 + T_S)                     Equation 3

Solving these three equations simultaneously we get:

T_F = 2 seconds

T_S = 4 seconds

Since, we have an answer for when the trajectories cross, we know for a fact that they indeed do cross.

The point of crossing can be found by using the value of T_F or T_S in the location matrices. Doing this for the first particle we get:

Location of path intersection = ( -1 + 2 , 4 - 2 , -1 + 2(2) )

Location of path intersection = ( 1 , 2 , 3)

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Two speakers are spaced 15 m apart and are both producing an identical sound wave. You are standing at a spot as pictured. What
IgorLugansk [536]

Answer:

Frequency is 213.04\ s^{-1}.

Explanation:

Distance between source 1 from the receiver , S_1 =\sqrt{10^2+22^2}=24.17\ m.

Distance between source 2 from the receiver , S_2=\sqrt{5^2+22^2}=22.56\ m.

Now ,

Path difference , r = S_1-S_2=24.17-22.56=1.61\ m.

We know, for constructive interference path difference should be integral multiple of wavelength .  

Therefore, r=n\times \lambda

It is given that n = 1,

Therefore, \lambda=1.61\ m.

Frequency can be found by , \nu=\dfrac{v}{\lambda}= \dfrac{343}{1.61}=   213.04\ s^{-1} .

Hence, this is the required solution.

5 0
3 years ago
A string under a tension of 36 N is used to whirl a rock in a horizontal circle of radius 3.6 m at a speed of 16.12 m/s. The str
ExtremeBDS [4]

Answer:

6010.457N

Explanation:

Centripetal acceleration = a= V²/R

At a radius of 3.6m and velocity of 16.12m/s,

Acceleration is

a = 16.12²/ 3.6 = 72.182 m/s²

Force = Mass (m) * Acceleration (a)

36 = m * 72.182

m = 36/72.182

At breaking point

Radius = 0.468 m and Velocity = 75.1 m/s

a = V²/R = 75.1²/0.468

a = 12051.3 m/s

F = Mass(m) * Acceleration (a)

F = m * 12051.3

m = F/ 12051.3

Settings the ratio of mass equal

m = m

=> 36/72.182 = F/12051.3

F = 12051.3 * 36/72.182

F = 6010.457N

3 0
3 years ago
The average coefficient of linear expansion of copper is 1.7 10-5 (°c)−1. the statue of liberty is 93 m tall on a summer morning
sammy [17]

Let the rise in temperature be 5^0C

The expansion in length due to change in temperature is given by the expression lαΔt , where l is the length, α is the  coefficient of linear expansion, Δt is the change in temperature.

Here l = 93 m, α = 1.7*10^{-5}  ^0C^{-1}, and Δt = 5^0C

So expansion in length = 93*1.7*10^{-5}*5 = 0.007905 m = 0.79*10^{-3}m

So order of magnitude in change in length = -3


3 0
3 years ago
Read 2 more answers
two 2.5 kg balls move away from each other one traveling 3 m/s to the right the other 4 m/s to the left what is the magnitude of
Juli2301 [7.4K]

Answer:

2.5 kg.m/s

Explanation:

Taking left side as positive while right side direction as negative then

Momentum, p= mv where m is the mass of the object and v is the velocity of travel

Momentum for ball moving towards right side=mv=2.5*-3=-7.5 kg.m/s

Momentum for the ball moving towards the left side=mv=2.5*4=10 kg.m/s

Total momentum=-7.5 kg.m/s+10 kg.m/s=2.5 kg.m/s

5 0
3 years ago
What can you infer about a wave with a short wavelength?
raketka [301]

Answer:

- It can be infer that it has a lower frequency.

<em>In the case of electromagnetic waves.</em>

- A short wavelength means a lower energy,

Explanation:

The wavelength is the distance between two consecutive crests or valleys while the frequency is the number of crests that pass for a specific point in an interval of time.

For example, a person makes laundry once a weak.

In this example, the event is represented by the laundry and the interval of time is once a weak

The velocity of a wave is defined as:

v = \nu \cdot \lambda  (1)

Where nu is the frequency and \lambda is the wavelenth

\lambda =  \frac{v}{\nu}  (2)

Notice from equation 2 that the wavelength is inversely proportional to the frequency (when the wavelength increases the frequency decreases).

In the case of electromagnetic waves, a short wavelength means a lower energy, as it can be seen in equation 4 (inversely proportional).

E = h\nu  (3)

E = \frac{hc}{\lambda} (4)

8 0
3 years ago
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