The maximum height is equal to 860.04m
Why?
We can find the maximum height of the object in two steps.
First step: Finding the initial speed.
[tex]v_{f}^{2}=v_{o}^{2}-2*g*d\\\\0=v_{o}^{2}-2*(9.81\frac{m}{s^{2}})*hmax\\\\hmax=\frac{v_{o}^{2}}{2*9.81\frac{m}{s^{2} }}[/tex]
Then,
[tex]v_{f}^{2}=v_{o}^{2}-2*g*d\\\\(75\frac{m}{s})^{2} =v_{o}^{2}-2*(9.81\frac{m}{s^{2}})*\frac{2}{3}\frac{v_{o}^{2}}{2*9.81\frac{m}{s^{2} }}\\\\5625\frac{m^{2} }{s^{2}}=v_{o}^{2}-\frac{2}{3}v_{o}^{2}\\\\3*5625\frac{m^{2} }{s^{2}}=v_{o}^{2}\\\\v_{o}=\sqrt{3*5625\frac{m^{2} }{s^{2}}}=129.90\frac{m}{s}[/tex]
Second step: Find the maximum height.
Now, again using the second equation, we need to subsitutite the obtained value for the initial speed into it, so:
[tex]hmax=\frac{(129.90\frac{m}{s})^{2}}{2*9.81\frac{m}{s^{2} }}=860.04m[/tex]
Hence, we have that the maximum height is equal to 860.04 meters.
Have a nice day!
