<p>can someone help me with this problem? thanks.</p>
<p>at time t=0, a ball was thrown upward from an initial height of 6 feet. until the ball hit the ground, its height, in feet, after t seconds was given by the function h(t)=c-(d-4t)^2, in which c and d are positive constants. if the ball reached its maximum height of 106 feet at time t=2.5, what was the height, in feet, of the ball at time t=1?</p>
<p>Use calc. The derivation at t=2.5 must be zero since thats when the ball reached its maximum height. Plug in what you get for d to find c. Then just find h(1).</p>
<p>Too lazy to do it out. If you need more help just ask.</p>
<p>f\'\'(x) = -acceleration (gravity)
f\'(0) = initial velocity
f(0) = initial height</p>
<p>now take integral of f\'\'(x), plug in what you kno to get constant
now again take integral of f\'(x) and plug in what you kno to get constant</p>
<p>now you have the equation for f(x).. using it you can figure out the height of the object at any time during its flight..</p>
<p>famous problem... its on almost all Physics tests..</p>
<p>uhh..this was one of the problems from an SAT practice test. there must be an easier way of doing it..</p>
<p>Mathwiz said it.
h(t)=c-(d-4t)^2
dh/dt h(t) = -2(d-4t)(4)=0 therefore d-4t=0 and t=2.5 so d=10
at h(0) = 6 = c-(10)^2 and so c = 106 and we know that d=10
h(1) = 106 - (10-4(1))^2 = 106-36 = 70ft</p>
<p>You can setup two equations, by just substituting in the given info.:</p>
<p>6=c-[d-4(0)]^2 or simply 6=c-(d)^2</p>
<p>AND</p>
<p>106=c-(d-10)^2 </p>
<p>You have now completely eliminated the (t) and have two equations with two variables c and d!</p>
<p>Now just solve for c in the first equation and you get:</p>
<p>c=(d)^2 + 6</p>
<p>Plug that into the second equation and you get:</p>
<p>106= [(d)^2 + 6] - [(d-10)^2]</p>
<p>Now you just have to solve for d!</p>
<p>What will hapen is once you expand the (d-10)^2, it will cancel the first d^2 and you'll get something like:</p>
<p>200=20d
d=10</p>
<p>Plug that back in to get c, and you'll get c=106.</p>
<p>Now plug everything back in and find the height plugging in what you now know for c, d, and t:</p>
<p>h(t)=106-[10-(4x1)]^2
h(t)=70</p>
<p>I know it looks complex but it's just solving a simple system of equations!</p>