# In the figure, water balloons are tossed from the roof of a building

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In the figure, 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.

The figure is a building with three angles that the balloon goes off. The first angle is a straight drop down from the roof. The second one is as if you threw the balloon from the roof straight out. The third one is throwing the water balloon up in the air from the roof. If you need more detail then that let me know.

Thanks

• They all have the same speed. They are all launched at the same speed, with the only force an acceleration straight down. The velocity will be different for all three, because velocity is a vector, but the speed will be identical.

The balloon launched straight up, neglecting air resistance, will peak at some height due to the acceleration of gravity, and begin accelerating downwards, achieving its launch speed again as it passes you. Thus it will have the same speed when it hits as the one launched straight down.

The one launched straight out will keep its original horizontal speed, and will accelerate in the same manner as the other two towards the ground. It’s final speed, unlike the other two, will be directed at an angle to the ground.

(Note: if air resistance were a factor, the one with the shortest path, the one launched straight down, would have the highest speed)

• The easiest way to determine the answer to this question is to use conservation of kinetic and potential energy. Since the initial height of the all the balloons is the same, all the balloons have the same initial potential energy. The fact that some of the balloons are moving horizontally does not affect their final kinetic energy. As the balloons move from the roof of the building to the ground, all of the potential energy is converted into kinetic energy. So, each balloon will have the same final kinetic energy. This means each balloon will have the same final speed. I have a computer program called Interactive Physics. I use this program to draw simulations of problems like this one. When I changed the angle, the final speed of each balloon was the same. That’s when I realized that conservation of kinetic and potential energy is the easiest way to determine the answer to this question.

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