Question

In Fig. 6-31, water balloons are tossed from the roof of a building, all with the same speed but with different launch angles. Which one has the highest speed when it hits the ground? Ignore air resistance. Explain your answer.

Fig. 6-31 Problem 12

Short answer

All three balloons will have the same speed on hitting the ground.

Step-by-step solution

Conservation of mechanical energy

When only internal forces do the work, and no work is done by external forces, then the mechanical energy of a system is conserved.

Comparing initial mechanical energy of all balloons

As all three balloons are initial at the same height, their initial potential energy will be equal. Similarly, as they all are fired with the same initial speed, their initial kinetic energy will also be equal.

That means that the total mechanical energy of all three balloons will be the same.

Applying conservation of mechanical energy

As there is no external air resistance, mechanical energy during the fall of any balloon will be conserved. The initial mechanical energy of each balloon is the same, and the change in gravitational potential energy for all the balloons is also the same (all thrown from the same initial height).

Thus, by conservation of mechanical energy, the final kinetic energy of all three balloons must be the same.