Question

A baseball is thrown up in the air from a height of 3 feet with an initial velocity of 23 feet per second. When does the baseball hit the ground?
A) -0.12 seconds
B) 1.44 seconds
C) 1.56 seconds
D) 1.79 seconds

Answer 1

Answer:

Step-by-step explanation:

This is information that is modeled by a parabolic equation.  The leading coefficient is -16t^2 because we are in feet as opposed to meters (which would be -4.9t^2).  The standard form of this parabolic motion is

$s(t)=-16t^2+v_{0}t+h_{0}$

where s(t) is the height of the baseball after a certain amount of time has gone by, v0 is the initial vertical velocity, and h0 is the initial height.  Filling in what we have:

$s(t)=-16t^2+23t+3$

We are asked when the ball hits the ground.  If s(t) is our position after a certain time has gone by, and the height of the ball on the ground is no height at all (or 0), then replace s(t) with 0 and factor to solve for t.

Throw that into the quadratic formula or however you like to factor second degree polynomials, and get that the 2 solutions are that

t = -.12 seconds and that t = 1.56 seconds.  We all know that time will NEVER be negative, so the time we want is 1.56 seconds, choice C.