What is its maximum altitude of the rocket?

Question

A rocket is launched vertically upward from Earth's surface at a speed of 5.3 km/s.

Answer 1

One of the kinematic equations of motion is:

v_f² = v_i² + 2a(x) where v_f is the final velocity, v_i is the initial velocity, "a" is the acceleration (in this case that is "g", the acceleration of gravity which is 9.81 m/s²), and "x" is the distance (in this case the altitude). So v_f = 0 (the rocket slows to an instantaneous stop when it reaches its maximum altitude), v_i = 5.3 km/s which we must convert to m/s to match our units for "g" making v_i = 5300 m/s, a = g = -9.81 m/s² resulting in:

0² = 5300² + 2(-9.81)(x)

0 = 28090000 - 19.62x

19.62x = 28090000

x = 1431702 m

converting this back to km by dividing by 1000 gives us 1432 km and then rounding to 2 significant figures results in an altitude of 1400 km.