Wile E. Coyote Lands in the River

Date: 08/20/99 at 17:28:42
From: Saddie
Subject: Velocity

Dr. Math:

I've tried to figure this problem out, but I've never been good at 
these velocity equations. Here's the problem:

"Wile E. Coyote is standing on a springboard atop a high cliff. 
Roadrunner drops a boulder on the other end of the springboard, 
sending Wile up with an initial velocity of 4 meters/sec. At what time 
will he land in the river, 120 m below the top cliff?" 

They give me the hint of using the equation h = -16t^2 + (v_o)t + s. 
What do I put in for the o and the s? I understand that that I am 
solving for t.

Please help! Thanks!

Date: 08/20/99 at 20:02:58
From: Doctor Ian
Subject: Re: Velocity

Hi Saddie, 

What this equation is saying, in English, is

  Your height at     Your original     your upward       your downward
  some moment, t  =  height         +  motion if      -  motion due to
                                       there were no     gravity
                                       gravity

                                                          1
         h        =  s              +  v  t           -   - gt^2
                                        o                 2
  
So 's' is Wile E.'s original height: 120 m above the river.

And 'v_o' is his 'original velocity' (or his 'velocity at time t = 0', 
depending on whether you want to read the subscript as an 'o' or a 
'0'): 4 m/s.

Can you take it from here? Be careful - the formula assumes that the 
value of g (the acceleration due to gravity) is 32 ft/sec^2 (half of 
which is 16 ft/sec^2), but the problem gives you everything in meters. 
The metric value of g is 9.8 m/sec^2.

Also, it's obviously a trick question - he won't land in the river at 
all. He'll hit the ground next to the river!

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/