# Math Help - antiderivatives

1. ## antiderivatives

A ball is thrown upward with an initial velocity of 64ft/sec from an initial height of 80ft. The acceleration due to gravity is -32ftsec^2

a. Write the velocity and position functions v(t) and y(t).
b. When does the ball hit the ground?
c. What is the maximum height obtained by the ball?

Need some help dont know where to start???
-thanks

2. Originally Posted by burton6
A ball is thrown upward with an initial velocity of 64ft/sec from an initial height of 80ft. The acceleration due to gravity is -32ftsec^2

a. Write the velocity and position functions v(t) and y(t).
Read v(t) as "velocity as a function of time." In plain english, velocity as a function of time is 1.) the initial velocity, upward, which we'll call +64 ft/s; and 2.) the velocity that results from constant (downward) acceleration, which we'll call (-32 ft/s^2)*t.

I don't know how rigid your instructor is about units, but it helps here to write the simple form of the formula without them:

$v(t) = 64 - 32t$

Now, the next bit actually involves your subject line. Can you figure out y(t) if I tell you $v(t) = dy/dt$ and $dy = v(t) dt$?