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**1. I just want to make sure I understand the concept correctly and that I have provided the correct explanation and understanding...therefore the image of the problem is not important**

"Figures 1 and 2 show the paths followed by two golf balls, A and B. In each figure, does Ball A spend more/the same/less time in the air than Ball B? In each figure, does Ball A have a greater/the same/smaller launch speed than Ball B?"

"Figures 1 and 2 show the paths followed by two golf balls, A and B. In each figure, does Ball A spend more/the same/less time in the air than Ball B? In each figure, does Ball A have a greater/the same/smaller launch speed than Ball B?"

**2. d=1/2gt^2 and d=vt**

**3. In the first figure, Ball A and Ball B are launched at different angles but the vertical components of the angles result in the same angle distance. If we recall from the text, a 60 degree and a 30 degree angle components result in the same vertical distance which is a similar analogy to the example in figure 1. While the horizontal distance of Ball B is greater, only the vertical distances of both balls depend on the time in the air. Therefore, both balls spend identical times in the air and you demonstrated this perfectly with the 1/2gt^2 distance equation.**

In the second figure, the vertical components of the angles do not result in the appropriate angles as in the previous example which resulted in the identical time of both balls in the air. This time, the vertical distance of Ball B is greater and therefore Ball B is in the air longer than Ball A. You again demonstrated how this fits into the equation 1/2gt^2 for the distance equation.

To figure out the launch speed, we only need to rely on the horizontal component of the angles as the horizontal component is independent and free of the vertical component. They work within their independent components rather being paired together. This is a vital concept to remember (the independence of the horizontal and vertical components). In the first figure, the horizontal distance of Ball B was demonstrated and can be seen by the image provided as Ball B travels a greater distance than Ball A. This greater horizontal distance infers in the faster launch speed for Ball B which you again neatly provide by the equation d=vt.

In the second figure, both balls land at the same spot and therefore have the same horizontal distance. Since the horizontal and vertical angles are independent of each other; the longer time in the air for Ball B would result in a faster launch speed for Ball B because as you stated, the greater height needs to be compensated. Ball A falls to the ground faster which results in the lower launch speed for Ball A.

In the second figure, the vertical components of the angles do not result in the appropriate angles as in the previous example which resulted in the identical time of both balls in the air. This time, the vertical distance of Ball B is greater and therefore Ball B is in the air longer than Ball A. You again demonstrated how this fits into the equation 1/2gt^2 for the distance equation.

To figure out the launch speed, we only need to rely on the horizontal component of the angles as the horizontal component is independent and free of the vertical component. They work within their independent components rather being paired together. This is a vital concept to remember (the independence of the horizontal and vertical components). In the first figure, the horizontal distance of Ball B was demonstrated and can be seen by the image provided as Ball B travels a greater distance than Ball A. This greater horizontal distance infers in the faster launch speed for Ball B which you again neatly provide by the equation d=vt.

In the second figure, both balls land at the same spot and therefore have the same horizontal distance. Since the horizontal and vertical angles are independent of each other; the longer time in the air for Ball B would result in a faster launch speed for Ball B because as you stated, the greater height needs to be compensated. Ball A falls to the ground faster which results in the lower launch speed for Ball A.