Question

Write and solve a quadratic equation for the situation below. Choose the answer that has both an equation that correctly models the situation as well as the correct solution for the situation.
A soccer ball is kicked from the ground toward the goalie with an initial velocity of 15 ft/s. If the ball is not caught by the goalie, how long will it take the ball to land on the ground?

a)None of the choices are correct.

b)0= −16t^2+t+15; t = 1 second

c)0= −16t^2+15t; t = 1 second

d)0= −4.9t^2+15t; t = t ≈ 3 seconds

Answer 1

Acceleration is:

a=g

Velocity is the integral of the above

v=gt+v0

And position is the integral of the above

h=gt^2/2+v0t+h0

You are given that v0=15ft/s and h0=0ft and let g≈-32 so

h(t)=-16t^2+15t

It will hit the ground when h(t)=0 so:

0=-16t^2+15t which is equal to

16t^2-15t=0  factor

t(16t-15)=0, since we are looking for the time other than zero...

t=15/16 of a second :)

So they obviously just rounded to one whole second.  So C.) was the correct answer.  (Although I would say they are all wrong because they didn't SAY to round the answer :P)   Haha, not trying to confuse you, the answer is most likely C. because they had the correct equation.