To calculate the maximum height attained by an object in free fall or projectile motion, we typically use the following kinematic equation:
\[ v^2 = u^2 + 2a s \]
where:
- \( v \) is the final velocity (at the maximum height, this is 0 m/s),
- \( u \) is the initial velocity (the velocity at launch),
- \( a \) is the acceleration (which is -g, or -10 m/s² in this case),
- \( s \) is the displacement (or maximum height, which we want to find).
Rearranging the formula for maximum height \( s \):
\[ s = \frac{v^2 - u^2}{2a} \]
Plugging in the values:
- \( v = 0 , \text{m/s} \)
- \( u = \) initial velocity (you would need to provide this value)
- \( a = -10 , \text{m/s}^2 \) (since the object is moving against gravity)
The formula simplifies to:
\[ s = \frac{0 - u^2}{2 \times (-10)} \] \[ s = \frac{u^2}{20} \]
So, the maximum height \( s \) depends on the initial velocity \( u \). If you provide the initial velocity, I can calculate the specific maximum height for you.
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