# Max height of thrown object with 12m/s at 1/5 of height

## Homework Statement

An object is shot vertically upward and has a speed of 12 m/s when it reaches one fifth of its maximum height.
a. What is the initial speed of the object?
b. What is the maximum height of the object?

## Homework Equations

Free falling objects

## The Attempt at a Solution

I used the formula vf^2 = vi^2 - 2g(yf - yi) and got 144 = 0 + 19.6(1/5 - 0), I solved for 1/5 so I have 144/19.6 = 1/5 and got 1/5 = 7.35 meters. This times 5 yields 36.73 meters. This would be it for part b. But I am stuck on part a where I have to find the speed. Any advise on how to approach this? Thank you.

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I used the formula vf^2 = vi^2 - 2g(yf - yi) and got 144 = 0 + 19.6(1/5 - 0)
You got a negative value (because -2g(yf - yi) is negative), and then you probably thought "oops, the square of velocity can't be negative, so let's change the sign and hope for the best". It does not work that way.

You should have asked yourself "why did I get a negative value where only a positive one is possible? Where did I go wrong"?

You got a negative value (because -2g(yf - yi) is negative), and then you probably thought "oops, the square of velocity can't be negative, so let's change the sign and hope for the best". It does not work that way.

You should have asked yourself "why did I get a negative value where only a positive one is possible? Where did I go wrong"?
Not really, the reason why I ended up with a positive value instead of a negative is because

144 = 0 - 2(-9.6)(1/5 height) = 144 = 0 -(-19.6)(1/5 height) = 144 = 19.6 (1/5 height). If you don't agree let me know.

Not really, the reason why I ended up with a positive value instead of a negative is because

144 = 0 - 2(-9.6)(1/5 height) = 144 = 0 -(-19.6)(1/5 height) = 144 = 19.6 (1/5 height). If you don't agree let me know.
The basic kinematic equation is $v_f^2 = v_i^2 + 2 a(s_f - s_i)$. Adapted to free fall, it is either $v_f^2 = v_i^2 + 2g (y_f - y_i)$, where $g$ is then taken negative, or $v_f^2 = v_i^2 - 2g (y_f - y_i)$, where $g$ is then taken positive. But you cannot have both the equation in the form $v_f^2 = v_i^2 - 2g (y_f - y_i)$ and $g$ negative in it.

I used the formula vf^2 = vi^2 - 2g(yf - yi) and got 144 = 0 + 19.6(1/5 - 0), I solved for 1/5 so I have 144/19.6 = 1/5 and got 1/5 = 7.35 meters. This times 5 yields 36.73 meters. This would be it for part b. But I am stuck on part a where I have to find the speed. Any advise on how to approach this? Thank you.
yf is not 1/5.
When the speed is zero, the object has reached the maximum height. (h_max).
When the speed is 12 m/s the object height is 1/5 from this maximum height.

1/5 is not a height in meters (or other unit of length) but a fraction.
Saying that 1/5=7.35 m is nonsense.