Explanation

Explanation

Explanation

To find the range (d) of a TV transmitter antenna, we use the line-of-sight formula:

d ≈ √(2 × h × R)  

Where:  

- d = distance to the horizon in kilometers  

- h = height of the antenna in kilometers  

- R = radius of Earth ≈ 6371 km  

Convert height:  

h = 100 m = 0.1 km  

Now plug in:  

d ≈ √(2 × 0.1 × 6371) ≈ √1274.2 ≈ 35.7 km  

So, the range is approximately 36 km

Explanation

10 machines * 5 days = 50 machine-days.

50 machine-days / 5 machines = 10 days

Explanation

The area of a square is calculated by multiplying the length of one side by itself.

In this case, the area is given as 4m^2.

To find the length of the square, we need to take the square root of the area.

The square root of 4 is 2.

Therefore, the length of the square is 2 meters.

Explanation

To find the power of the combination of lenses, we can use the formula:

P_total = P1 + P2

Where:

- P_total is the total power of the combination

- P1 is the power of the convex lens

- P2 is the power of the concave lens

The power of a lens is given by the formula:

P = 1 / f

Where:

- P is the power of the lens

- f is the focal length of the lens

Given that the focal length of the convex lens is 40 cm and the focal length of the concave lens is -25 cm (negative because it is concave), we can calculate their respective powers:

P1 = 1 / 40 cm = 0.025 dioptres (approximately)

P2 = 1 / -25 cm = -0.04 dioptres (approximately)

Now, we can calculate the total power of the combination:

P_total = P1 + P2

= 0.025 dioptres + (-0.04 dioptres)

= -0.015 dioptres / -1.5  (approximately)

(0.015 = 1.5= 0.015 * 100= 1.5)

Explanation

The centripetal force necessary to keep the racing car in its circular path is indeed provided by friction between the tires of the car and the track.

Concept:

When the car is moving in a circular path, it experiences an inward acceleration towards the center of the circle.

This acceleration is called the centripetal acceleration.

According to Newton's second law of motion, the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

In this case, the net force is the centripetal force, and the centripetal acceleration can be calculated using the formula:

a_c = v^2 / r

Where:

- a_c is the centripetal acceleration

- v is the speed of the car

- r is the radius of the circular track

Substituting the given values into the formula:

a_c = (50.0 m/s)^2 / 250 m

Simplifying the equation:

a_c = 2500 m^2/s^2 / 250 m

a_c = 10 m/s^2

The centripetal force required to keep the car in its circular path is equal to the product of the car's mass and the centripetal acceleration.

Using the given mass of the car:

F = (2.00 x 10^3 kg) * (10 m/s^2)

Simplifying the equation:

F = 2.00 x 10^4 N

Therefore, the centripetal force necessary to keep the car in its circular path is provided by friction and its value is 2.00 x 10^4 Newtons.

Explanation

When Bilal moves away from a stationary organ producing a sound of frequency 'f' with a speed equal to 0.5 times the speed of sound, he will hear a sound of lower frequency.

This phenomenon is known as the Doppler effect.

To calculate the frequency of the sound Bilal hears, we can use the following formula:

f' = f * (v + vL) / (v + vS)

Where:

- f' is the frequency of the sound heard by Bilal

- f is the frequency of the sound produced by the stationary organ

- v is the speed of sound

- vL is the speed of Bilal

- vS is the speed of the source (in this case, the stationary organ)

Since Bilal is moving away from the source, vS is negative.

We substitute the values into the formula:

f' = f * (v - 0.5v) / (v - (-v))

Simplifying the equation:

f' = f * (0.5v) / (2v)

f' = f * 0.5 / 2

f' = f * 0.25

Explanation

To calculate the force exerted by the pavement on the tires, we can use the centripetal force formula:

Force (F) = (Mass (m) * Velocity squared (v^2)) / Radius (r)

Given:

Mass (m) = 1000 kg

Velocity (v) = 10 m/s

Radius (r) = 10 m

 Calculate the centripetal force (F):

Using the formula, F = (m * v^2) / r, we can substitute the given values to find the force:

F = (1000 kg * (10 m/s)^2) / 10 m

F = 100,000 N / 1.0 x 10^4 N

Explanation

To find the period and wavelength of a wave, we can use the formulas:

Period (T) = 1 / Frequency (f)

Wavelength (λ) = Speed (v) / Frequency (f)

Given:

Frequency (f) = 2.5 Hz

Speed (v) = 1.5 m/s

Step 1: Calculate the period (T):

Using the formula, T = 1 / f, we can substitute the given frequency to find the period:

T = 1 / 2.5 Hz

T = 0.4 s

Therefore, the period of the wave is 0.4 seconds.

Step 2: Calculate the wavelength (λ):

Using the formula, λ = v / f, we can substitute the given speed and frequency to find the wavelength:

λ = 1.5 m/s / 2.5 Hz

λ = 0.6 m

Therefore, the wavelength of the wave is 0.6 meters.

In summary, the wave has a period of 0.4 seconds and a wavelength of 0.6 meters.