Question

An object take 5s to reach the ground from the height of 5 m on the planet what is the value explain by solving​

Answer 1

Correct Question:

An object takes 5 s to reach the ground from a height of 5 m on a planet. What is the value of g on the planet?

Answer:

The value of g on the planet is 0.4 m / s².

Explanation:

Given data:

Initial velocity ( u ) = 0 m / s.

Displacement ( s ) = 5 m.

Time ( t ) = 5 s.

To find:

Acceleration due to gravity ( g ) = ?

Solution:

According to Newton's second equation of motion for freely falling objects,

$s \: = \: \frac{1}{2} \: g \: {t}^{2} \\ \\ \implies \: 5 \: = \: \frac{1}{2} \: g \: \times \: {5}^{2} \\ \\ \implies \: 5 \: = \: \frac{1}{2} \: g \: \times \: 5 \: \times \: 5 \\ \\ \implies \: 5 \: \times \: 2 \: = 25 \: g \\ \\ \implies \: 10 \: = \: 25 \: g \\ \\ \implies \: g \: = \: \frac{10}{25} \\ \\ \implies \: g \: = \: \frac{2}{5} \\ \\ \therefore \: \boxed{g \: = \: 0.4 \: m \: / {s}^{2}} \: ( \sf \: on \: the \: planet \: )$

Ans.: The value of g on the planet is

0.4 m / s².

Additional Information:

1. Acceleration due to gravity:

The acceleration produced in an object due to the gravitational force of earth is called as acceleration due to gravity.

It is denoted by g.

It's value is 9.8 m / s² on the earth. This value of g changes on earth from lower heights to higher heights.

2. Free fall:

When an object falls from a height due to only the earth's gravitational force, it is called as free fall.

3. Newton's equations of motion for freely falling objects:

A. Newton's First Equation of Motion for freely falling objects:

$\boxed{v = g\:t}$

B. Newton's Second Equation of Motion for freely falling objects:

$\boxed{s \: = \: \frac{1}{2} \: g \: {t}^{2}}$

C. Newton's Third Equation of Motion for freely falling objects:

$\boxed{v^{2}=2\:g\:s}$

Where,

$\sf\:u \: \longrightarrow \: Initial\:velocity\\\\ \sf\:v \: \longrightarrow \: Final\:velocity\\\\ \sf\:g \: \longrightarrow \:Acceleration\:due\:to\:gravity\\\\\sf\:s \: \longrightarrow \: Displacement\\\\\sf\:t \: \longrightarrow \: Time$