I really don't understand algebra or word problems...please help!

Question

A water balloon is tossed into the air with an upward velocity of 25 ft/s. Its height h(t) in ft after t seconds is given by the function h(t) = − 16t^2 + 25t + 3. 



After how many seconds will the balloon hit the ground? (hint: Use the quadratic formula)


What will the height be at t = 1 second

Answer 1

To find out after how many seconds the balloon hits the ground, set h(t)=0.  The equation now becomes

 

0 = -16t² + 25t + 3

 

 

Solve for t using the quadratic formula:

 

t = (-b ± √(b² - 4ac)) / 2a

 

where:

a = -16

b = 25

c = 3

 

Plug in these values into the formula to solve for t.  You will obtain 2 values of t.  Pick the most reasonable, and logical value.

 

 

To find the height at 1 second, set t=1 to solve for h(t).

Answer 2

Using the quadratic formula, one value of t will be negative. That value is obviously not the correct answer. The positive value of t will be the correct response.

As for word problems, don't let them confuse you. A word problem simply presents a scenario, a description of a circumstance in which a problem occurs. Your task is to separate the math from the scenario & solve the problem. Many such problems can involve confounding variables that you can ignore. This one, for example, does not clarify whether the balloon is thrown straight up or at a particular angle. It doesn't matter, because your teacher wants you to practice using the quadratic formula to solve this kind of problem. Just do the math & don't think too deeply about the details. Good luck!