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## Homework Statement

A pitcher throws a ball towards a wall that's 85 feet away from him. The ball's initial speed is 5 feet/second, and the acceleration of the ball is 32 feet/sec^2. How long does the ball travel before hitting the wall?

## Homework Equations

distance = rate * time

## The Attempt at a Solution

So the speed of the ball I have as:

[t = time]

5 + 32t

Which I believe makes sense because the ball is initially traveling @ 5 ft/sec, and after 1 second, the ball is traveling 37 ft/sec, then after 2 seconds the ball is traveling @ 69 ft.sec, etc.

I assume we use d = rt (which is distance = rate * time).

So the total distance the ball travels is 85 feet which is equal to the total rate of 5 + 32t * time. The equation I set up like this:

85 = (5 + 32t) * t

I set up the quadratic like so:

32t^2 + 5t - 85 = 0

I solved it and got:

(1/64) * (sqrt(10905) - 5) which is approx. 1.55.

I worked it out to check, and 1.55 seconds is much too low for the value:

5 feet + (32 feet * 2 seconds) = 69 feet

So after 2 seconds, the ball has only traveled 69 feet, while the quadratic equation states that the ball has traveled 85 feet after 1.55 seconds.

What gives?