Question 56
<pre><font face = "courier new" size = 2 sp = 1><b>How would you set up the following word problem: You are
hitting baseballs. When tossing the ball into the air, your
hand is 5 feet above the ground. You hit the ball when it 
falls back to a height of 4 ft. If you toss the ball with 
an initial velocity of 25ft/sec, how much time will pass 
before you hit the ball? Thanks!

Use the formula h = h<sub>0</sub> + v<sub>0</sub>t - 16t<sup>2</sup> since distance is given
in feet. (If distance were in meters, we would have to use
4.9 where the 16 is).

h<sub>0</sub> represents the initial height. v<sub>0</sub> represents the initial 
velocity, and h is height at the instant when t seconds have
elapsed.

>>...When tossing the ball into the air, your hand is 5 feet 
above the ground...<<

So h<sub>0</sub> = 5

>>...you toss the ball with an initial velocity of 25ft/sec...<<

So v<sub>0</sub> = 25

So we substitute 5 for h<sub>0</sub> and 25 for v<sub>0</sub>, making our formula

h = 5 + 25t - 16t<sup>2</sup>

>>...You hit the ball when it falls back to a height of 4 ft...<<

So we wish to find t (the number of seconds) has elapsed at the
instant when the ball is 4 feet high, so we substitute 4 for h
and solve for t:

4 = 5 + 25t - 16t<sup>2</sup>

16t<sup>2</sup> - 25t - 1 = 0

Use quadratic formula, get solutions  

-.04 and 1.6.  We ignore the negative answer.  So the answer is

1.6 seconds approximately.

Edwin