how to find A in quadratic projectile motion

Question

what would the standard form be for this question? During a drumline performance, a drummer throws his drumstick with an upward velocity of 32 feet per second. if the drummer releases and catches the drumstick 6 feet above the ground, what is the maximum height of the drumstick? how long is the drumstick in the air? what i cant figure out is what the ax^2 is i can get the bx and the c but not the A. please help.

Answer 1

Hint: Assume the height function is $$f(t) = at^2 + bt + c\tag{1}$$ Then you have three initial conditions: $$f''(0) = -32 \tag{2}$$ $$f'(0)=32\tag{3}$$ $$f(0)=6\tag{4}$$

These conditions should allow you to determine the unknown coefficients of $f$.

Answer 2

Your Equation for this kind of problem is

$s(t) = –gt^2 + v_0t + h_0$

$g$ is Gravity (half gravity) you were given a velocity in terms of feet per second so we will go with $16$ for this value

$v$ is initial velocity which you were given as $32$

$h$ is your initial height which is $6$ ft

So your equation is

$s(t) = -16t^2 + 32t + 6$