Prove that 3:8 is equivalent to 12:32:
I'd suggest that you write the ratio 12:32 as<span /><span><span><span><span><span><span><span><span><span>12</span><span /></span><span><span>32</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span></span>
and then factor both the 12 and the 32. Write out the factors:<span /><span><span><span><span><span><span><span><span><span>12</span><span /></span><span><span>32</span><span /></span><span><span /><span /></span></span></span><span>=</span><span><span><span><span><span>(</span><span>?</span><span>)</span><span>(</span><span>?</span><span>)</span></span><span /></span><span><span><span>(</span><span>?</span><span>)</span><span>(</span><span>?</span><span>)</span></span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span></span> and then reduce this last result by cancelling out the common factor.3 x 4 = 12 8 x 4 = 32 It is equivalent. They both multiplied by four the get that ratio.
so hmm check the picture below, thus the ball hits 19 feet of height twice, once on the way up, and once on the way down, at about 0.64 seconds and at 1.17 seconds.
