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

Algebra ->  Quadratic Equations and Parabolas -> 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       Log On


   

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) About Me  (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 v=10 and c=3. So the equation is h=+-16t%5E2%2B10t%2B3

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 h=0 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.



h=+-16t%5E2%2B10t%2B3 Start with the given equation.


0=+-16t%5E2%2B10t%2B3 Plug in h=0


Notice we have a quadratic equation in the form of at%5E2%2Bbt%2Bc where a=-16, b=10, and c=3


Let's use the quadratic formula to solve for t


t+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


t+=+%28-%2810%29+%2B-+sqrt%28+%2810%29%5E2-4%28-16%29%283%29+%29%29%2F%282%28-16%29%29 Plug in a=-16, b=10, and c=3


t+=+%28-10+%2B-+sqrt%28+100-4%28-16%29%283%29+%29%29%2F%282%28-16%29%29 Square 10 to get 100.


t+=+%28-10+%2B-+sqrt%28+100--192+%29%29%2F%282%28-16%29%29 Multiply 4%28-16%29%283%29 to get -192


t+=+%28-10+%2B-+sqrt%28+100%2B192+%29%29%2F%282%28-16%29%29 Rewrite sqrt%28100--192%29 as sqrt%28100%2B192%29


t+=+%28-10+%2B-+sqrt%28+292+%29%29%2F%282%28-16%29%29 Add 100 to 192 to get 292


t+=+%28-10+%2B-+sqrt%28+292+%29%29%2F%28-32%29 Multiply 2 and -16 to get -32.


t+=+%28-10+%2B-+2%2Asqrt%2873%29%29%2F%28-32%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


t+=+%28-10%2B2%2Asqrt%2873%29%29%2F%28-32%29 or t+=+%28-10-2%2Asqrt%2873%29%29%2F%28-32%29 Break up the expression.


t=-0.222 or t=0.847 Use a calculator to approximate the answers.


Since a negative time value does NOT make sense, this means that the only solution is t=0.847


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.