SOLUTION: HELP!!! tonisha hit a ball into the air with an initial velocity of 48 feet per second. the height h in feet of the ball above the ground can be modeled by h=-16t squared+48t+2,

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: HELP!!! tonisha hit a ball into the air with an initial velocity of 48 feet per second. the height h in feet of the ball above the ground can be modeled by h=-16t squared+48t+2,      Log On


   

Question 85825: HELP!!!
tonisha hit a ball into the air with an initial velocity of 48 feet per second. the height h in feet of the ball above the ground can be modeled by h=-16t squared+48t+2, where t is the time in seconds after tonisha hit the ball. find the time it takes the ball to reach 38 feet above the ground.
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
The problem tells you that the equation for the height of the ball is:
.
h+=+-16t%5E2+%2B+48t+%2B+2
.
It asks you to find the time that the ball reaches a height of 38 feet.
.
Substitute 38 feet into the equation. Since 38 feet is the height, it replaces h in the
equation, and the equation becomes:
.
38+=+-16t%5E2+%2B+48t+%2B+2
.
The standard form for solving equations of this type is:
.
at%5E2+%2B+bt+%2B+c+=+0
.
in which a, b, and c are integers.
.
You can work the height equation into this form. Begin by transposing (switching sides) of
the height equation to get:
.
-16t%5E2+%2B+48t+%2B+2+=+38
.
Next subtract 38 from both sides of the equation:
.
-16t%5E2+%2B+48t+%2B+2+-+38+=+0
.
and after the subtraction the left side becomes:
.
+-16t%5E2+%2B+48t+-36+=+0
.
Notice that this equation now matches the standard form ... in which a = -16, b = +48, and
c = -36.
.
You can simplify this a little by noting that 4 is a factor of all the terms. So divide
all the terms in this equation by 4 to get:
.
-4t%5E2+%2B+12t+-+9+=+0
.
You can further simplify this by multiplying all the terms on both sides by -1 to get:
.
4t%5E2+-+12t+%2B+9+=+0
.
This can be solved by using the quadratic formula, or you might notice that the left side
of this equation factors to give:
.
%282t+-3%29%5E2+=++0
.
The equation will be true when the left side equals zero. Therefore, it will be true if
2t+-+3+=+0
.
Solve this equation by adding 3 to both sides to get:
.
+2t+=+3
.
and solve for t by dividing both sides by 2 to get:
.
t+=+3%2F2+=+1.5+ seconds.
.
So the ball reaches a height of 38 feet 1.5 seconds after Tonisha hits it.
.
Hope this helps you to understand the problem.