An experimental model rocket has a mass of 0.054kg. The fuel that was used in one test had 215J of chemical potential energy. When the rocket reached an altitude of 119m, it was travelling at 48m/s and still rising. With what efficiency did the rocket convert chemical potential energy into mechanical energy.

Eg = 0.045 X 9.81X119 = 62.9 Joul

Ek= 1/2 m v^2 = .5 X 0.054 x 48^2 = 62.2 Joul
ETotal = 62.9 + 62.2 = 125.1 J
Efficiency = 125.1 / 215 = 58 %

Eg = 0.045 X 9.81X119 = 62.9 Joul

Ek= 1/2 m v^2 = .5 X 0.054 x 48^2 = 62.2 Joul
ETotal = 62.9 + 62.2 = 125.1 J
Efficiency = 125.1 / 215 = 58 %

total useful energy=mg*119+1/2 m 48^2

chem energy=215J

efficiency=useful energy/total chem energy

To find the efficiency with which the rocket converted chemical potential energy into mechanical energy, we need to calculate the mechanical energy gained by the rocket and compare it to the chemical potential energy that was initially stored.

First, we need to calculate the total mechanical energy gained by the rocket. This includes both the kinetic energy (KE) and the gravitational potential energy (PE) at its maximum height.

1. Kinetic Energy (KE):
The kinetic energy of the rocket can be calculated using the formula:
KE = (1/2) * m * v^2
where m is the mass of the rocket and v is its velocity.

Substituting the given values:
m = 0.054 kg (mass of the rocket)
v = 48 m/s (velocity of the rocket)
KE = (1/2) * 0.054 kg * (48 m/s)^2

2. Gravitational Potential Energy (PE):
The gravitational potential energy of the rocket at its maximum height can be calculated using the formula:
PE = m * g * h
where m is the mass of the rocket, g is the acceleration due to gravity, and h is the height.

Substituting the given values:
m = 0.054 kg (mass of the rocket)
g = 9.8 m/s^2 (acceleration due to gravity)
h = 119 m (maximum height reached by the rocket)
PE = 0.054 kg * 9.8 m/s^2 * 119 m

Now, we can calculate the total mechanical energy gained by adding the kinetic energy and the gravitational potential energy:
Total Mechanical Energy = KE + PE

Next, we can calculate the efficiency of the rocket by dividing the mechanical energy gained by the initial chemical potential energy:
Efficiency = (Total Mechanical Energy / Initial Chemical Potential Energy) * 100%

Substituting the values we have calculated:
Efficiency = (Total Mechanical Energy / 215 J) * 100%

Now, you can plug in the values and calculate the efficiency of the rocket.