# A new projectile launcher is developed in the year 2023

A new projectile launcher is developed in the year 2023 that can launch a 104 kg spherical probe with an initial speed of 6000m/s. For testing purposes, objects are launched vertically.
(a) Neglect air resistance and assume that the acceleration of gravity is constant. Determine how high the launched object can reach above the surface of Earth.
(b) If the object has a radius of 20cm and the air resistance is proportional to the square of the object’s speed with cw = 0.2, determine the maximum height reached. Assume the density of air is constant.
(c) Now also include the fact that the acceleration of gravity decreases as the object soars above Earth. Find the height reached.
(d) Now add the effects of the decrease in air density with altitude to the calculation. We can very roughly represent the air density by log10 (p) = – 0.05h + 0.11 where p is the air density in kg/m3 and h is the altitude above Earth in km. Determine how high the object now goes.