Suppose a 0.04-kg car traveling at 2.00 m/s can barely break an egg. What is the min

Response:

a) 318.2 W/m^2

b) 2.5 x 10^-4 J

c) 1.55 x 10^-8 v/m

Reasoning:

The laser power P = 1 mW = 1 x 10^-3 W

duration t = 250 ms = 250 x 10^-3 s

Taking a beam diameter of 2 mm = 2 x 10^-3 m

therefore

the beam's cross-sectional area A = = (3.142 x )/4

A = 3.142 x 10^-6 m^2

a) The intensity I = P/A

where P refers to the laser's power

and A represents the beam's cross-sectional area

I = ( 1 x 10^-3)/(3.142 x 10^-6) = 318.2 W/m^2

b) The total energy delivered E =Pt

where P is the beam's power

and t is the exposure duration

E = 1 x 10^-3 x 250 x 10^-3 = 2.5 x 10^-4 J

c) The peak electric field can be computed as

E =

where I signifies the beam's intensity

and E is the electric field

c is the speed of light = 3 x 10^8 m/s

= 8.85 x 10^9 m kg s^-2 A^-2

E = = 1.55 x 10^-8 v/m

Answer:

Responses to the 3.17 punchline varied among many individuals, with some suggesting that it was a "full" moon day which prevented the astronauts from landing.

Others claimed that the astronauts took off during daylight hours when the moon was not visible. There were also comments that indicated that 'astro' refers to stars rather than satellites, explaining why they did not land.

A few even noted that 'astro naut' sounds like 'naught,' meaning zero (0), as a possible reason for their failure to land.

When the boat submerges completely in the pond, the water level of the pond rises.

Since you've completed parts a and b, I will tackle part c.
For part C
To respond to this question, we must identify the zeros of the velocity function:

This polynomial can be factored:

Finding the zeros now becomes straightforward since the function equals zero when any factor is zero.

By solving these equations, we identify our zeros:

The particle remains stationary at t=0 and t=3/2.
For part D
We must discover when the velocity function exceeds zero. We will utilize its factored form.
We will assess when each factor is greater than zero and compile the findings in the following table:

From the table, it's evident that our function is positive when and t>3/2.
This indicates the interval during which the particle moves forward.
For part E
The distance traveled can be represented as:

We simply substitute t=12 to calculate the total distance traveled:

For part F
Acceleration is defined as the rate at which velocity changes.
We determine acceleration by deriving the velocity function concerning time.

To find the acceleration at 1 second, we substitute t=1s into the previous equation:

Answer:

Explanation:

The wavelength of sound can be calculated using the formula: wavelength = velocity / frequency.

Thus, it becomes:

λ = 340 / 170

λ = 2 m.

When the person stands ideally in the center between the speakers, the sound waves reaching him are perfectly aligned (no path difference), resulting in maximum sound intensity.

As he moves closer to one of the speakers, his proximity to that speaker increases while the distance to the other speaker decreases, creating a path difference in the sound waves reaching his ears.

If he walks 0.5 m toward one speaker, the created path difference becomes:

0.5 x 2 = 1 m.

This path difference equals λ / 2, leading to destructive interference, resulting in minimal sound being audible.

As he continues walking a full 1 m, the created path difference totals 2 m.

This corresponds to a path difference of λ, causing constructive interference and maximum sound perception.

Finally, if he moves an additional 1.5 m, the resulting path difference increases to 3 m.

Thus, we arrive at a path difference of 3 λ / 2, producing destructive interference once more, leading to minimum sound being perceived again.

In summary, the man begins at a maximum intensity point, moves to minimum intensity, then back to a maximum, and ultimately ends at another minimum sound intensity position.