Answer :
Using the work-energy theorem, we find that without air resistance, the model rocket would have reached a height of 138.5 meters instead of the 118 meters it achieved with air resistance.
The question deals with the concepts of work, energy, and motion in Physics. The work done by air resistance is given to be -672 J, which means that this amount of energy was taken away from the rocket due to air resistance. When the rocket reaches its maximum height of 118 m, we can use the work-energy theorem to find the potential energy at the highest point and thus determine the height it would have achieved without air resistance.
First, let's calculate the potential energy at the maximum height with air resistance:
- Potential energy (PE) = m imes g imes h
- PE = 3.25 kg imes 9.8 m/s2 imes 118 m
- PE = 3739 J
This is the energy the rocket has after air resistance has done work. To find the total energy without air resistance, we simply add the work done by the air resistance to the potential energy:
- Total energy without air resistance = PE + Work done by air resistance
- Total energy without air resistance = 3739 J + 672 J
- Total energy without air resistance = 4411 J
Now, we find the height it would achieve without air resistance:
- 4411 J = 3.25 kg imes 9.8 m/s2 imes h' (h' is the new height)
- h' = 4411 J / (3.25 kg imes 9.8 m/s2)
- h' = 138.5 m
Thus, without air resistance, the rocket would have reached a height of 138.5 meters.
