Algebra Demystified 2nd Ed

Chapter 11 QuaDraTiC appliCaTionS 409

✔SOLUTIONS
For all of these problems, both a negative t and a positive t will be solutions
for the quadratic equations. Only the positive t will be a true solution.

1. For the formula h = –16t^2 + v 0 t + h 0 , h 0 = 56 and v 0 = 0 (because the object
   is being dropped). The object reaches the ground when h = 0.
   h = –16t^2 + 56
   0 = –16t^2 + 56
   16 t^2 = 56
   t^2 =^56
   16

t^2 =^7

2

t =^7

2

t≈ 18 7.

The object will reach the water in about 1.87 seconds.

2. For the formula h = –16t^2 + v 0 t + h 0 , h 0 = 240 and v 0 = 0 (because the
   object is being dropped). The object reaches the ground when h = 0.
   h = –16t^2 + 240
   0 = –16t^2 + 240
   16 t^2 = 240
   t^2 =^240
   16
   t^2 = 15
   t = 15
   t ≈ 38 7.
   The object will reach the ground in about 3.87 seconds.


3. For the formula h = –16t^2 + v 0 t + h 0 , h 0 = 70 and v 0 = 0 (because the object
   is being dropped). The object reaches the ground when h = 0.
   h = –16t^2 + 70
   0 = –16t^2 + 70
   16 t^2 = 70