We can solve the problem by using the law of conservation of energy:
- at the beginning, all mechanical energy of the object is just kinetic energy: [tex]K=\frac{1}{2}mv^2[/tex], where m is the mass and v is the velocity
- at the point of maximum height, all mechanical energy of the object is just gravitational potential energy: [tex]U=mgh[/tex], where h is the maximum height
Therefore, the conservation of energy becomes:
[tex]\frac{1}{2}mv^2 = mgh[/tex]
Re-arranging, we find the maximum height:
[tex]h=\frac{v^2}{2g} = \frac{(75.0 m/s)^2}{2(9.8 m/s^2)}=287.0 m[/tex]
