Quadratic functions and word probs: Suppose a baseball is

C

cakers44

New member
Joined
Oct 11, 2006
Messages
14
Suppose a baseball is shot up from the ground straight up with an initial velocity of 32 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0

• 16 represents ½g, the gravitational pull due to gravity (measured in feet per second 2).
• v0 is the initial velocity (how hard do you throw the object, measured in feet per second).
• s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.

a) The ball will be how high above the ground after 1 second? (Is the answer to this 16?)

b) How long will it take to hit the ground?

c) What is the maximum height of the ball?
 
a baseball is shot up from the ground straight up with an initial velocity of 32 feet per second.
Click to expand...

so, v<sub>o</sub> = 32 and s<sub>o</sub> = 0 ... your equation is

s(t) = -16t<sup>2</sup> + 32t

the height at t = 1 second will be s(1).

the graph of s(t) is an inverted parabola ... the max height will occur at its vertex.
do you remember how to find the vertex of a parabola? hint: x = -b/(2a)

to find how long it takes to hit the ground, set s(t) = 0 and solve for t.
 
Hello, Skeeter. I am still confused. Solving the equation

s(t) = -16t(squared) + 32t
s(1) = -16(1)squared + 32(1)
s= -16 + 32
s=16

What am I doing wrong?[/quote]
 
You have to solve for 't' to get the total time the ball was in the air.

-16t^2 + 32t = 0
t = 0 and 2

this means the ball hit the ground in two seconds.
When you put in s(1) your answer is the height of the ball after 1 second.
Use Skeeter's hint to find max height.
 
and when you get to: -16t^2 + 32t = 0
you can make your life a little easier by multiplying by -1 (means change signs):
16t^2 - 32t = 0 ; then divide by 16:
t^2 - 2t = 0 ; then factor:
t(t - 2) = 0
 
Guys, finding the vertex of this parabola confuses me. When I use the formula, I get the answer to be 1. but that can't be right, can it?

Help!
 
yes ... t = 1 is when the ball reaches maximum height.

the ball leaves the ground and it takes 2 seconds to return to the ground ... now, use your common sense ... how long does it take for the ball to get as high as it's gonna go?
 
You must log in or register to reply here.
Top