A student solving a physics problem for the range of a projectile has obtained the expression r= v20sin(2θ)g where v0=37.2meter/

Answer:

The ratio of mass that is discarded is determined by this equation:

M - m = (3a/2)/(g²- (a²/2) - (ag/2))

Explanation:

The force acting on an object in motion is defined by the equation:

F = ma

Additionally, there is a gravitational force consistently acting downwards on the object, defined as g = 9.8 ms⁻²

For convenience, we will utilize a positive notation for downward acceleration and a negative notation for upward acceleration.

Case 1:

The hot air balloon has mass = M

Acceleration = a

Upward thrust from hot air = F = constant

Gravitational force acting downward = Mg

The net force on the balloon can be expressed as:

Ma = Gravitational force - Upward Force                              

Ma = Mg - F                      (since the balloon moves downward, that means Mg > F)

F = Mg - Ma

F = M (g-a)

M = F/(g-a)

Case 2:

After releasing the ballast, the new mass becomes m. The new upward acceleration is -a/2:

The net force is expressed as:

-m(a/2) = mg - F        (The balloon is moving upwards, hence F > mg)

F = mg + m(a/2)

F = m(g + (a/2))

m = F/(g + (a/2))

Determining the fraction of the mass initially dropped:

Answer: The calorimeter's heat capacity is

Explanation:

This scenario assumes the amount of heat lost by the hot object equals the amount of heat gained by the cold object.

where,

= specific heat capacity of water =

= specific heat capacity of calorimeter =?

= mass of water = 108.7 g

= mass of calorimeter = 108.7 g

= final temperature of the mixture =

= initial temperature of the water =

= initial temperature of calorimeter =

Now substituting all provided values into the formula, we obtain

Hence, the heat capacity of the calorimeter is

Response: The spring constant is 25 N/m.

Details:

The body’s mass is 25 g, which converts to 0.025 kg (since 1 kg = 1000 g).

The total oscillations are 20 in 4 seconds.

Oscillations per second =

Spring's frequency of vibration is =

The spring constant 'k' can be derived from the relationship involving frequency, mass, and spring constant.

The spring constant is 25 N/m.

The right answer is (a).

Solar panels create electric current through the photoelectric effect, which describes how photons strike certain material surfaces, resulting in the release of electrons when light with the correct frequency hits them. A photon will interact with an electron on the panel, causing it to be ejected from the panel's surface.

As the illumination on the panel becomes brighter, the intensity of the light rises, indicating an increase in the number of photons. Each photon has the potential to liberate an electron; thus, as the number of incoming photons rises, so does the quantity of freed electrons. Given that the photoelectric current reflects the rate at which these electrons flow, an increase in light intensity leads to a corresponding rise in the photoelectric current.

If the frequency of the light is increased without a change in brightness, the photoelectric current remains the same because the total number of photons does not increase. Yet, the electrons that are ejected do escape with higher kinetic energy. However, since the total number of electrons liberated stays unchanged, the current remains constant regardless of the electrons' increased energy. Thus, option b is incorrect.

Increasing the wavelength of the light means the energy of the photons decreases. This would cause the emitted electrons to have lower energy. However, if the brightness is consistent, the number of electrons remains the same, and as a result, there would be no change in the photoelectric current. Therefore, choice (c) is also incorrect.

The correct answer is (a). To generate the needed current, the brightness of the incident light must be increased.