a atapult launcher on an aircraft carrier accelerates a jet from rest to 72m/s. The work done catapult during the launch is 7.6 x 10 to the 7th J. a)What is the mass of the jet? b) If the jet is in contact with the catapult for 2s, what is the power output of the catapult?

a) Well, I'm glad the jet got catapulted and not a cat! To find the mass of the jet, we can use the work-energy theorem. The work done is equal to the change in kinetic energy. So, we can write:

Work = (1/2) * mass * velocity^2

Given that the work done is 7.6 x 10^7 J and the final velocity of the jet is 72 m/s, we can rearrange the equation to solve for mass:

mass = (2 * Work) / velocity^2

Plugging in the values, we get:

mass = (2 * 7.6 x 10^7 J) / (72 m/s)^2

mass ≈ 139.43 kg

So, the mass of the jet is approximately 139.43 kg.

b) Ah, power! The rate at which work is done. The power output of the catapult can be calculated by dividing the work done by the time taken. In this case, the time taken is 2 seconds. So, we have:

Power = Work / Time

Plugging in the values, we get:

Power = 7.6 x 10^7 J / 2 s

Power = 3.8 x 10^7 W

So, the power output of the catapult is approximately 3.8 x 10^7 Watts. That's quite a "watt-astic" amount of power!

And remember, if you ever need help launching a cat-apult, just let me know!

To find the mass of the jet, we can use the work-energy principle, which states that the work done on an object is equal to its change in kinetic energy.

a) The work done on the jet is 7.6 x 10^7 J, and the change in kinetic energy can be calculated using the formula:

ΔKE = KE_final - KE_initial

Since the jet starts from rest, the initial kinetic energy (KE_initial) is zero. Therefore, the change in kinetic energy (ΔKE) is the same as the final kinetic energy (KE_final).

ΔKE = KE_final = 1/2 * m * v^2

Where:
m = mass of the jet
v = final velocity of the jet = 72 m/s

Plugging in the given values, the equation becomes:

7.6 x 10^7 J = 1/2 * m * (72 m/s)^2

Now, let's solve for the mass (m):

7.6 x 10^7 J = 0.5 * m * 5184 m^2/s^2

Divide both sides by 5184 to isolate mass (m):

m = (7.6 x 10^7 J) / (0.5 * 5184 m^2/s^2)
m ≈ 2927 kg

Therefore, the mass of the jet is approximately 2927 kg.

b) The power output of the catapult can be calculated using the formula:

Power = Work / Time

Given:
Work = 7.6 x 10^7 J
Time = 2 s

Plugging in the values:

Power = (7.6 x 10^7 J) / (2 s)
Power = 3.8 x 10^7 W

Therefore, the power output of the catapult is 3.8 x 10^7 Watts.

To find the mass of the jet, we can use the work-energy principle. The work done by the catapult is equal to the change in kinetic energy of the jet.

a) The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. Mathematically, it can be expressed as:

Work = Change in Kinetic Energy

Given that the work done by the catapult is 7.6 x 10^7 J and the change in kinetic energy is equal to the initial kinetic energy (since the jet starts from rest), we can write:

7.6 x 10^7 J = (1/2)mv^2

Where:
m = mass of the jet (unknown)
v = final velocity of the jet (72 m/s)

Plugging in the given values, the equation becomes:

7.6 x 10^7 J = (1/2)m(72^2)

Simplifying the equation:

7.6 x 10^7 J = 2592m

Now, solve for m:

m = (7.6 x 10^7 J) / 2592

Calculating m:

m ≈ 29380.25 kg

Therefore, the mass of the jet is approximately 29,380.25 kg.

b) To calculate the power output of the catapult, we can use the equation:

Power = Work / Time

Given that the work done by the catapult is 7.6 x 10^7 J and the time taken for the jet to be launched is 2 seconds, we can substitute the values into the equation:

Power = (7.6 x 10^7 J) / 2 s

Calculating the power:

Power = 3.8 x 10^7 W

Therefore, the power output of the catapult is approximately 3.8 x 10^7 Watts.

A)

m*v^2=kinetic energy
m*72^2=7.6*10^7
m*(7.6*10^7)/(72^2)=14660.5kg

B)
p=w/t
p=(7.6*10^7)/2=3.8*10^7
p=38000000 watts