Having problems with this optimization problem pleace help thanks!?

Question

How many seconds would it take for a ball that was launcehd vertically upward in the air from the ground with the initial velocity of 256 feet per second to reach its maximum height? What is the maximum height?

Answer 1

sounds like a basic physics question. Start with the equation for velocity - it should include a term for initial velocity and acceleration (gravity). You know both. Solve for Velocity = 0 (maximum height is where the ball slows to a stop, just before it begins to fall).

The final part should be clear from here.

Answer 2

shouldn't there be a difference in the results, if i use different balls?

Answer 3

The position formula should be handy in this one.  p(t) = gt^2+ vt +a.  Where g is the acceleration of gravity (-32ft/s^2), v is the initial velocity, given as 256ft/s and a is the initial position, which I assume is ground level, so a=0.  Phew! Another formula we need is the velocity, which can be derived by taking the derivative of the position function (if you know Calculus) or I can just tell you it is v(t) = 2gt+ v.  Now, we know that at it's highest point, the ball stops moving, so it's velocity is zero.  0 = v(t) = 2(-32)t + 256.  Solving for this gives us, t=4.  This is the time it takes for the ball to reach its highest point.  But we need the height, or position.  We plug 4 back into the position function to get p(4) = (-32)(16)+(256)(4) =  512 ft.