SOLUTION: I would like to know if you would be able to help me with this problem. using this equation: h= -16t^2+vt+c Problem- a child tosses a ball upward with a starting velocity of

Question 176934This question is from textbook Algebra 1
: I would like to know if you would be able to help me with this problem.
using this equation:
h= -16t^2+vt+c
Problem- a child tosses a ball upward with a starting velocity of 10 ft/s from a height of 3 ft.
b) solve. if not caught how long will the ball be in air?
Thank you for any help you can offer me!
Thank you so much!!
-j2012
This question is from textbook Algebra 1

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since we have a "starting velocity of 10 ft/s from a height of 3 ft", this means that and . So the equation is

The ball will be in the air as long as the height h is NOT zero (when the ball is on the ground). So if we plug in and solve for t, we'll find when the ball hits the ground. From there, we can figure out how long it will be in the air.

Start with the given equation.

Plug in

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for t

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

or Break up the expression.

or Use a calculator to approximate the answers.

Since a negative time value does NOT make sense, this means that the only solution is

So when the time is approximately 0.847 seconds, the ball will hit the ground.

So this means that the ball will be in the air for about 0.847 seconds.
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