a ball is dropped from a heiht of 100 feet one second later another ball is dropped from a height of 75 feet .which ball hits the ground first???

Question

anonymous · Answer

equation for first is 
$$h(t)=100-16t^2$$

anonymous · Answer

after one second it is 84 feet yes?

anonymous · Answer

and it's velocity is 
$$h'(1)=-32$$

anonymous · Answer

so i guess the new equation, starting at t = 1 is 
$$h(t)=84-32t-16t^2$$

anonymous · Answer

other one has equation 
$$h(t)=75-16t^2$$

anonymous · Answer

see which gets to zero first

anonymous · Answer

if i knew would i ask you???

anonymous · Answer

what i mean is set each equation above = 0 and solve.

anonymous · Answer

whatever is time is least is the first to get there.  i.e. solve 
$$84-32t-16t^2=0$$ and 
$$75-16t^2=0$$

anonymous · Answer

first one gives 
$$t=\frac{3}{2}$$

anonymous · Answer

second one gives 
$$\frac{5\sqrt{3}}{4}$$ which is bigger than 1.5

anonymous · Answer

so first ball hits ground first\??

anonymous · Answer

1st ball falls in 4.47s(approx)
2nd in 3.8s.
so if the 2nd ball is thrown 1 second later...
the 1st ball should fall first.