Final answer:
The maximum height of the golf ball can be found by applying the principle of conservation of energy, equating the total mechanical energy at the point of launch to the total mechanical energy at the maximum height and solving for the new height.
Step-by-step explanation:
To find the maximum height of the golf ball, we can use the principle of conservation of energy. The total mechanical energy (kinetic + potential) at the launch point will be equal to the total mechanical energy at the maximum height.
When the golf ball is launched, it has both kinetic energy due to its speed and potential energy due to its height above the ground. The kinetic energy is calculated using the formula ½ m v2, and the potential energy is calculated using m g h, where m is the mass of the ball, v is the velocity, g is the acceleration due to gravity (9.8 m/s2), and h is the height.
At the maximum height, the ball will have a new potential energy and a kinetic energy related to its new speed of 12 m/s.
Initial total energy (Ei) = Potential energy at launch + Kinetic energy at launch
Final total energy (Ef) = Potential energy at max height + Kinetic energy at max height
By setting Ei = Ef and solving for the new height (hmax), we can find the maximum height of the golf ball:
½ m vlaunch2 + m g hlaunch = ½ m vmax height2 + m g hmax height