Question

At some planet, $g=1.96m{{s}^{-2}}$. If it is safe to jump from a height of 2m on the earth, then the corresponding safe height on that planet is:
A. 2m
B. 5m
C. 10m
D. 20m

Answer 1

Hint: The acceleration is the rate of change of velocity with respect to time and when this acceleration is studied under the effect of gravity, then this acceleration is called acceleration due to gravity. We will find the safe height on the other planet is calculated by using the equation of motion.

Formula used:
The equation of motion used is given as:
${{v}^{2}}-{{u}^{2}}=2aS$

Complete Answer:
The acceleration due to gravity is denoted by g. It is different for different planets depending on their radius and velocities. The acceleration due to gravity is studied under the effect of gravity. The motion under the effect of gravity can be expressed by replacing a by g in the equation of motion.
Here, we use the 3rd equation of motion, in which S is replaced by height, and acceleration by acceleration due to gravity g. therefore, we have
${{v}^{2}}-{{u}^{2}}=2gh$
In the question, it is given that the acceleration due to gravity, and height. Also, for the other planet g is given.
${{g}_{e}}=9.8m{{s}^{-2}},h=2m$
${{g}_{p}}=1.96m{{s}^{-2}}$
Now using equation of motion we have:
$\begin{align}
  & {{v}^{2}}-{{u}^{2}}=2gh \\
 & {{v}^{2}}-0=2\times 9.8\times 2 \\
 & {{v}^{2}}=39.2m{{s}^{-2}} \\
\end{align}$
This velocity is attained by other planet, then the height for that planet is calculated as:
$\begin{align}
  & {{v}^{2}}-{{u}^{2}}=2gh \\
 & 39.2-0=2\times 1.96\times h \\
 & h=39.2/3.9 \\
 & h=10m \\
\end{align}$
Therefore, the height for the other planet is 10m.

Hence, option C is the correct option.

Note:
The acceleration due to gravity g for the earth is fixed. The acceleration due to gravity for other planets is also given in the question. We will use equations of motion to find the safe height of jump on another planet, using the respective g values.