Answer to Question #102926 in Mechanics | Relativity for Emilie

Question

Kinematics
A dust particle kicked by Neil Armstrong on the moon leaves the lunar surface travelling at 2.0 m/s upwards. It moves upwards to a maximum height and then begins to falling back downwards. When it return to neils waist height on its descent( a height of 120cm above the lunar surface) it is falling at 33 cm/s

Determine the acceleration
Maximum height
And how long it takes from being kicked upwards to reach neils waist height on its descent

Answer 1

From the coservation of energy:

$$0.5mv^2=0.5mu^2+mah$$

Acceleration:

$$a=\frac{v^2-u^2}{2h}=\frac{2^2-0.33^2}{2(1.2)}=1.6\frac{m}{s^2}$$

Maximum height:

$$H=\frac{v^2}{2(a)}=\frac{2^2}{2(1.6)}=1.25\ m$$

$$t=t_1+t_2=\frac{v}{a}+\frac{u}{a}=\frac{v+u}{a}$$

$$t=\frac{2+0.33}{1.6}=1.46\ s$$