Question

#26 question



An astronaut jumps to a height of 5.00m above the surface of the moon. If the acceleration due to gravity on the moon is 1.6 m/s², how long does it take for the astronaut to fall to the surface of the moon?


A. 1.01s
B. 2.48s
C. 3.09s
D. 6.17s ​

Answer 1

So, the time that taken for the astronaut to fall to the surface of the moon is 2.5 s.

Introduction

Hi ! In this question, I will help you. In this question, you will learn about the fall time of the free fall motion. Free fall is a downward vertical motion without being preceded by an initial velocity. When moving in free fall, the time required can be calculated by the following equation:

$\sf{h = \frac{1}{2} \cdot g \cdot t^2}$

$\sf{\frac{2 \cdot h}{g} = t^2}$

$\boxed{\sf{\bold{t = \sqrt{\frac{2 \cdot h}{g}}}}}$

With the following condition :

• t = interval of the time (s)
• h = height or any other displacement at vertical line (m)
• g = acceleration of the gravity (m/s²)

Problem Solving

We know that :

• h = height = 5.00 m
• g = acceleration of the gravity = 1.6 m/s²

What was asked :

• t = interval of the time = ... s

Step by step :

$\sf{t = \sqrt{\frac{2 \cdot h}{g}}}$

$\sf{t = \sqrt{\frac{2 \cdot 5}{1.6}}}$

$\sf{t = \sqrt{6.25}}$

$\boxed{\sf{t = 2.5 \: s}}$

Conclusion

So, the time that taken for the astronaut to fall to the surface of the moon is 2.5 s.

See More

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• The speed of the object at a certain height (free fall motion) https://brainly.com/question/26377041
• The relationship between acceleration and the change in velocity and time in free fall https://brainly.com/question/26486625