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A ball is thrown straight upward from the surface of the Moon. Is the maximum height it reaches less than, equal to, or greater than the maximum height reached by a ball thrown upward on Earth with the same initial speed? (Ignore air resistance in both cases.) Explain.

Verified Answer :

Answer:

greater

Explanation:

Let the initial velocity is u .

Acceleration due to gravity on earth, ge = g

Acceleration due to gravity on moon, gm = g / 6

Let the maximum height reached on earth is h and the maximum height reached on the moon is h'.

Use third equation of motion

\(v^{2}=u^{2}- 2gh\)

At maximum height, the final velocity = 0.

For earth

0 = u^2 - 2 gh

h = u^2 / 2g ..... (1)

For moon

0 = u^2 - 2 g/6 x h'

h' = 6u^2 /  2g = 6 h     (From (1)

So, the maximum height reached at moon is 6 times the maximum height reached at earth.

The maximum height it reaches on the Moon is greater than the maximum height reached on the Earth.

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Further explanation

Acceleration is rate of change of velocity.

\(\large {\boxed {a = \frac{v - u}{t} } }\)

\(\large {\boxed {d = \frac{v + u}{2}~t } }\)

a = acceleration ( m/s² )

v = final velocity ( m/s )

u = initial velocity ( m/s )

t = time taken ( s )

d = distance ( m )

Let us now tackle the problem!

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We will use following formula to solve this problem:

\(v^2 = u^2 - 2gh\)

\(0^2 = u^2 - 2gh\)

\(u^2 = 2gh\)

\(\large {\boxed {h = \frac{u^2}{2g}}}\)

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From above formula , we can conclude that the maximum height is inversely proportional to the gravitational acceleration.

Gravitation acceleration on the moon is less that gravitational acceleration on the earth. Therefore , the maximum height it reaches on the Moon is greater than the maximum height reached on the Earth.

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Learn more

  • Velocity of Runner : https://brainly.com/question/3813437
  • Kinetic Energy : https://brainly.com/question/692781
  • Acceleration : https://brainly.com/question/2283922
  • The Speed of Car : https://brainly.com/question/568302

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Answer details

Grade: High School

Subject: Physics

Chapter: Kinematics

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Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Projectile , Motion , Horizontal , Vertical , Release , Point , Ball , Wall

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