1. ## integration problem

here is the question, with what initial velocity must an object be thrown upward (from ground leve) to reach the top of the washington monument (550ft.) use a(t)=-32ft/sec^2

thanks

2. Originally Posted by soldatik21
here is the question, with what initial velocity must an object be thrown upward (from ground leve) to reach the top of the washington monument (550ft.) use a(t)=-32ft/sec^2

thanks
$\displaystyle v_0$ = initial velocity

$\displaystyle v = v_0 - 32t$

when it reaches the top, $\displaystyle v = 0$

let T be the time it reaches the top ...

$\displaystyle T = \frac{v_0}{32}$

$\displaystyle 550 = \int_0^T v_0 - 32t \, dt$

solve for $\displaystyle v_0$

3. i understand everything you posted but how would i take the integral of Vo-32t?

4. If you're integrating with respect to t, than all your other variables are considered constant:

$\displaystyle \int Rtdt = \frac{Rt^2}{2}$

Edit: And to add some nonesense.

$\displaystyle \int a(t)dt = v(t) = -32t + c = Vi - 32t$

$\displaystyle Vi - 32t = 0$

$\displaystyle t = \frac{Vi}{32}$

$\displaystyle \int v(t)dt = s(t) = Vit - 16t^2 + c = Vit - 16t^2$

$\displaystyle 550 = Vit - 16t^2$

$\displaystyle 550 = Vi \frac{Vi}{32} - 16 (\frac{Vi}{32})^2$

$\displaystyle Vi = 200 \sqrt {22}$