# projectile motion problem

• Apr 27th 2009, 08:15 PM
nmound
projectile motion problem
This is the problem:
A Ball is thrown into the air with an initial velocity of 64 feet per second. the height of the ball(in feet) [I]t[I] seconds after it is shot into the air is given by the function h(t)=-16t^2+64t

a)How many seconds after the ball is thrown does it reach its maximum height and what is this height?

b) How many seconds after the ball is thrown does it hit the ground?

I do not have a clue how to solve this
• Apr 27th 2009, 08:21 PM
Jhevon
Quote:

Originally Posted by nmound
This is the problem:
A Ball is thrown into the air with an initial velocity of 64 feet per second. the height of the ball(in feet) [i]t[i] seconds after it is shot into the air is given by the function h(t)=-16t^2+64t

a)How many seconds after the ball is thrown does it reach its maximum height and what is this height?

you want the t-value for the vertex of the parabola.

can you continue?

Quote:

b) How many seconds after the ball is thrown does it hit the ground?
set h(t) = 0 and solve for t. the larger t-value is what you want

can you continue?
• Apr 27th 2009, 08:23 PM
nmound
how do i find the vertex of the parabola. and as far as setting h(t) to zero and solving, i dont have to plug in anything else?
• Apr 27th 2009, 08:29 PM
Jhevon
Quote:

Originally Posted by nmound
how do i find the vertex of the parabola. and as far as setting h(t) to zero and solving, i dont have to plug in anything else?

for a parabola $\displaystyle y = ax^2 + bx + c$, the vertex occurs when $\displaystyle x = \frac {-b}{2a}$

of course, here, your $\displaystyle y = h(t)$ and your $\displaystyle x = t$