A 20.0-kg model plane flies horizontally at a constant speed of 12.2 m/s.

(a) Calculate its kinetic energy.
. J
(b) The plane goes into a dive and levels off 20.0 m closer to Earth. How much potential energy does it lose during the dive? Assume no additional drag.
J
(c) How much kinetic energy does the plane gain during the dive?
J
(d) What is its new kinetic energy?
J
(e) What is its new horizontal velocity?
m/s
-i got at 1488.4

KE =m•v²/2 =20•12.2²/2 =1488 J.

ΔPE = m•g•Δh = 20•9.8•20 = 3920 J.
Δ KE = ΔPE = 3920 J.
KE1 =KE + Δ KE = 1488 +3920= 5408 J.
The horizontal velocity isn’t changed. The vertical component is appeared, therefore, the velocity (as the vector sum of horizontal and vertical components) is increased.

To calculate the kinetic energy of the model plane, we can use the formula:

Kinetic energy = 1/2 * mass * velocity^2

Given:
Mass (m) = 20.0 kg
Velocity (v) = 12.2 m/s

(a) Now, let's calculate its kinetic energy:

Kinetic energy = 1/2 * 20.0 kg * (12.2 m/s)^2
Kinetic energy = 1/2 * 20.0 kg * 148.84 m^2/s^2
Kinetic energy = 1488.4 J

Therefore, the kinetic energy of the plane is 1488.4 J.

(b) When the plane goes into a dive and levels off 20.0 m closer to Earth, it loses potential energy. The potential energy lost can be calculated using the formula:

Potential energy lost = mass * g * change in height

Given:
Change in height (Δh) = -20.0 m (negative sign indicates a decrease in height)
Acceleration due to gravity (g) = 9.8 m/s^2

Potential energy lost = 20.0 kg * 9.8 m/s^2 * (-20.0 m)
Potential energy lost = -3920 J

Therefore, the potential energy lost during the dive is 3920 J.

(c) The potential energy lost is converted into kinetic energy. So, the kinetic energy gained during the dive is equal to the potential energy lost. Thus,

Kinetic energy gained = 3920 J

(d) To find the new kinetic energy of the plane, we need to add the kinetic energy gained during the dive to the initial kinetic energy.

New kinetic energy = Initial kinetic energy + Kinetic energy gained
New kinetic energy = 1488.4 J + 3920 J
New kinetic energy = 5408.4 J

Therefore, the new kinetic energy of the plane is 5408.4 J.

(e) The horizontal velocity remains constant during the dive. Therefore, the new horizontal velocity will still be 12.2 m/s.

Hence, the new horizontal velocity of the plane is 12.2 m/s.

(a) To calculate the kinetic energy of the model plane, you can use the formula:

Kinetic Energy (KE) = (1/2) * mass * velocity^2

Given:
Mass (m) = 20.0 kg
Velocity (v) = 12.2 m/s

Substituting the given values into the formula:

KE = (1/2) * 20.0 kg * (12.2 m/s)^2

Calculating the result:

KE = 0.5 * 20.0 kg * 148.84 m^2/s^2
= 2982.8 J

Therefore, the kinetic energy of the model plane is 2982.8 J.

(b) The potential energy lost by the plane during the dive can be calculated using the formula:

Potential Energy (PE) = mass * gravity * height

Given:
Mass (m) = 20.0 kg
Height (h) = 20.0 m (changed altitude)
Gravity (g) = 9.8 m/s^2 (approximation)

Substituting the given values into the formula:

PE = 20.0 kg * 9.8 m/s^2 * 20.0 m

Calculating the result:

PE = 3920 J

Therefore, the potential energy lost by the plane during the dive is 3920 J.

(c) The kinetic energy gained during the dive can be calculated by subtracting the initial kinetic energy from the potential energy lost:

Kinetic Energy Gained = Potential Energy Lost - Initial Kinetic Energy

Given:
Potential Energy Lost = 3920 J
Initial Kinetic Energy = 2982.8 J

Calculating the result:

Kinetic Energy Gained = 3920 J - 2982.8 J
= 937.2 J

Therefore, the kinetic energy gained during the dive is 937.2 J.

(d) The new kinetic energy can be calculated by adding the gained kinetic energy to the initial kinetic energy:

New Kinetic Energy = Initial Kinetic Energy + Kinetic Energy Gained

Given:
Initial Kinetic Energy = 2982.8 J
Kinetic Energy Gained = 937.2 J

Calculating the result:

New Kinetic Energy = 2982.8 J + 937.2 J
= 3920 J

Therefore, the new kinetic energy of the plane is 3920 J.

(e) To determine the new horizontal velocity, you need to use the conservation of energy principle, assuming no additional drag. Since the kinetic energy is directly proportional to the square of the velocity, the new horizontal velocity can be calculated by taking the square root of the ratio of the new kinetic energy to the initial kinetic energy, multiplied by the initial velocity.

New Velocity = sqrt((New Kinetic Energy / Initial Kinetic Energy) * Velocity^2)

Given:
New Kinetic Energy = 3920 J
Initial Kinetic Energy = 2982.8 J
Velocity = 12.2 m/s

Calculating the result:

New Velocity = sqrt((3920 J / 2982.8 J) * (12.2 m/s)^2)
= sqrt(1.313 * 148.84 m^2/s^2)
≈ sqrt(195.3692 m^2/s^2)
≈ 13.987 m/s

Therefore, the new horizontal velocity of the plane after the dive is approximately 13.987 m/s.