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### Wile E. Coyote Lands in the River

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Date: 08/20/99 at 17:28:42
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.

```

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

What this equation is saying, in English, is

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/
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Associated Topics:
High School Physics/Chemistry
High School Puzzles

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