Question

a) If a person can jump a maximum horizontal distance (by using a 45° projection angle) of 2.85 m on Earth, what would be his maximum range on the Moon, where the free-fall acceleration is g/6 and g = 9.80 m/s2? m(b) Repeat for Mars, where the acceleration due to gravity is 0.38g. m

Answer 1

Given,

The angle of projection, θ=45°

The maximum horizontal distance the person can jump on earth, R_e=2.85 m

The acceleration due to the gravity of earth, g=9.80 m/s²

The acceleration due to gravity on the moon, g_m=g/6

The acceleration due to gravity on the mars, g_mr=0.38g

The maximum range of a projectile on earth is given by,

$R_e=\frac{u^2}{g}$

Where u is the maximum initial velocity with which the person can jump.

On substituting the known values,

$\begin{gathered} 2.85=\frac{u^2}{9.80} \\ u=\sqrt[]{2.85\times9.80} \\ =5.28\text{ m/s} \end{gathered}$

a)

The maximum range on the moon is given by,

$R_{}m=\frac{u^2}{g_m}$

On substituting the known values,

$\begin{gathered} R_m=\frac{5.28^2}{\frac{9.80}{6}} \\ =17.07\text{ m} \end{gathered}$

Thus the maximum range on the moon would be 17.07 m

b)

The maximum range on the mars is given by,

$\begin{gathered} R_{mr}=\frac{u^2}{g_{mr}} \\ =\frac{u^2}{0.38g} \end{gathered}$

On substituting the known values,

$\begin{gathered} R_{mr}=\frac{5.28^2}{0.38\times9.80} \\ =7.49\text{ m} \end{gathered}$

Thus the maximum range on the mars is 7.49 m