Physics

The correct result is 11.48 m (to 2 decimal places). The proper rounding is 11.5 m/s, not 11.4 m/s ;-)

there are a lot of ways to solve this problem, we can use the second law of motion which is : (final velocity)^2 - (initial velocity)^2 = 2 acc.due to gravity distance(height)

And since the final velocity which is at the max. height equals Zero and the initial velocity = 15, Then 0 - (15)^2 = 2 9.8 max.height = (-15)^2 = 19.6*height =225 = 19.6h Max. Height = 225/19.6 = 11.4 approx.

As we suppose conservation of mechanical energy:

$v^2=2gh=225=19.6\cdot{}h\Rightarrow{}h=\frac{225}{19.6}\cong{}11.5$

If you want, multiply by $\text{m}$ so your result is not dimensionless.

Use conservation of mechanical energy

$\Large \frac{1}{2}mv^2 = mgh$

$\Large \Rightarrow h= \frac{v^2}{2g} = \frac{15^2}{2\times 9.8} =11.4$ (m)

Using the formula to calculate the maximum height of the body , we find the answer as 11.47m.

Vf^2 = Vi^2 + 2ad

Thus, finding d,

d = (Vf^2-Vi^2)/2a Hence, d = [0^2-(15^2)]/2(9.8) consider absolute value for distance with reference upward d = 11.4 m/s

Hint: Use Newton's third equation of motion and put the final velocity as 0. The result will surprise you!!!