Question

An astronaut drops a hammer from 2.0 meters above the surface of the moon. if the acceleration due to gravity on the moon is 1.62 meters per second 2, how long will it take for the hammer to fall to the moon's surface

Answer 1

Answer:

1.57 s

Explanation:

Since the motion of the hammer is a uniformly accelerated motion, the distance covered by the hammer in a time t is

$S=\frac{1}{2}at^2$

Where, in this case

S = 2.0 m is the distance covered

a = 1.62 m/s^2 is the acceleration due to gravity

t is the time taken

Re-arranging the equation, we can find the time the hammer takes:

$t=\sqrt{\frac{2S}{a}}=\sqrt{\frac{2(2.0 m)}{1.62 m/s^2}}=1.57 s$

Answer 2

The time taken by the hammer to fall on the surface of the moon is  $\boxed{1.57\,{\text{s}}}$.

Further Explanation:

Given:

The acceleration due to gravity on the surface of the moon is  $1.62\,{{\text{m}} \mathord{\left/{\vphantom {{\text{m}} {{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace} {{{\text{s}}^{\text{2}}}}}$.

The height from which the hammer falls towards the surface is  $2\,{\text{m}}$.

Concept:

The hammer falls freely without action of any force or any friction of the medium. It will fall freely under the acceleration due to gravity on the surface of the moon.

The motion of the hammer freely under the gravity is governed by the second equation of motion. The second equation of motion can be written as:

$\boxed{S=ut+\frac{1}{2}a{t^2}}$

Here, $S$ is the distance through which the hammer falls, $u$ is the initial speed of the hammer and $a$ is the acceleration due to gravity on the surface of moon.

Since the hammer is just dropped, the initial velocity of the hammer will be zero.

Substitute the values in the above expression.

$\begin{aligned}2&=\left( {0 \times t}\right)+\left( {\frac{1}{2}\times 1.62 \times {t^2}}\right) \\t&=\sqrt {\frac{{2 \times 2}}{{1.62}}} \,{\text{s}}\\&= 1.{\text{57}}\,{\text{s}}\\\end{aligned}$

Thus, the time taken by the hammer to fall on the surface of the moon is  $\boxed{1.57\,{\text{s}}}$.

Learn More:

1. Suppose our experimenter repeats his experiment on a planet more massive than earth brainly.com/question/10934170

2. Derive a formula for the mass of a planet in terms of its radius r brainly.com/question/2289465

3. What is the magnitude fcont of the force that the car exerts on the truck? Use the coordinate system shown in part b brainly.com/question/2235246

Answer Details:

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords:  Astronaut, drops a hammer, surface of moon, acceleration due to gravity, equation of motion, time taken by hammer, to fall, force, friction, freely under gravity.