Calc prob. I know how to solve using d(t) = vt + 16t^2 but that's not the point of the assignment. I need to somehow incorporate derivatives/integrals so could someone explain how I would do that please?

Question

math2400 · Answer

An object is thrown off of a 480ft building with initial velocity of -64 ft/sec. With what velocity does the object hit the ground?

anonymous · Answer

starting with gravity?

anonymous · Answer

gravity is a constant, $-32$ feat per second squared i.e. it is acceleration 
it is the derivative of the velocity is $-32$ so $$v=32t+
v_0$$ as you know $v(0)=-64$ you have $v_0=-64$ and so 
$$v(t)=-32t-64$$

anonymous · Answer

feet, not feat

anonymous · Answer

then the position is the anti derivative of the velocity, so 
$$h(t)=-16t^2-64t+h_0$$ and since $h(0)=480$ you know $$h(t)=-16t^2-64t+480$$

anonymous · Answer

it hits the ground when $h(t)=0$ solve $-16t^2-64t+480=0$ and get $t=-2+\sqrt{34}$

anonymous · Answer

finally to find the velocity when it hits the ground, compute 
$$v(2-\sqrt{34})$$

math2400 · Answer

Thank yoU!!! I completely forgot about this! You're the best!