Question

for a final project in seons physics class, students were instructed to build a water balloon launcher, write a hypothesis, and then carry out an experiment with the launcher. considering that 90 degrees means launching the balloon straight up into the air and 0 degrees means launching it straight along the ground, seon first wrote the hypothesis below.
if the angle at which the balloon is launched decreases from 90 degrees, then the distance that the balloon goes along the ground will increase, because more energy will go into pushing the balloon forward than upward.
seon found that this was true until the angle reached about 45 degrees, and then the distance along the ground began to decrease again. seon knows that he will need to write a new explanation, but he would like to conduct an experiment that is based on his original
how could seon rewrite his hypothesis to be a statement that will more likely be supported?
change the independent variable to \if the angle at which the balloon is launched increases up to 90 degrees...\
change the dependent variable to \if the angle at which the balloon is launched moves closer to 45 degrees...\
change the independent variable to \if the angle at which the balloon is launched moves closer to 45 degrees...\
change the dependent variable to \if the angle at which the balloon is launched increases to 90 degrees...\

Explanation:

In projectile motion (which this water - balloon launch is related to), the range (distance along the ground) of a projectile (assuming no air resistance and constant initial velocity) is given by the formula \(R=\frac{v^{2}\sin2\theta}{g}\), where \(v\) is the initial velocity, \(\theta\) is the launch angle, and \(g\) is the acceleration due to gravity. The function \(y = \sin2\theta\) has a maximum when \(2\theta=90^{\circ}\) (i.e., \(\theta = 45^{\circ}\)). So, the range first increases as the angle decreases from \(90^{\circ}\) to \(45^{\circ}\) and then decreases as the angle further decreases below \(45^{\circ}\). To make the hypothesis more likely to be supported, we should base it on the behavior of the range around the angle that gives the maximum range. The independent variable is the launch angle (\(\theta\)), and we want to focus on the region around \(45^{\circ}\) where the range has its maximum.

Answer:

change the independent variable to “If the angle at which the balloon is launched moves closer to 45 degrees...”