A shuttlecock is launched from the ground with an initial speed of 37.2044 m/s at an angle of 8.8162 degrees with respect to the horizontal. The shuttlecock experiences air resistance with a drag coefficient of 0.2903 in an environment where the air density is 0.1313 kg/m3. If the shuttlecock has a radius of 3.4 cm and a mass of 5.2 grams, what is the maximum height reached by the shuttlecock? Assume that the experiment is done near the surface of the earth.

A shuttlecock is launched from the ground with an initial speed of 37.2044 m/s at an angle of 8.8162 degrees with respect to the horizontal. The shuttlecock experiences air resistance with a drag coefficient of 0.2903 in an environment where the air density is 0.1313 kg/m3. If the shuttlecock has a radius of 3.4 cm and a mass of 5.2 grams, what is the maximum height reached by the shuttlecock? Assume that the experiment is done near the surface of the earth.