Question

An object hits a wall and bounces back with half of its original speed. what is the ratio of the initial kinetic energy to the final kinetic energy?

Answer 1

The ratio of the initial kinetic energy to the final kinetic energy is 4:1

Kinetic energy (KE) is given as $\frac{1}{2} mv^{2}$ i.e. it is proportional to $v^{2}$ i.e. the square of speed. 

We write the initial kinetic energy is KE.1 =(1/2)mu^2 

When speed is halved, speed will be u/2,

then final kinetic energy will be KE.2 = ( 1/2)m[u/2]^2  = (1/8)mu^2 

Now,ON SOLVING  K,E1 /K.E2, WE GET =  4:1

Answer 2

The ratio of the initial kinetic energy to the final kinetic energy is 4 : 1

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Further explanation

Let's recall Kinetic Energy Formula as follows:

$\large {\boxed{Ek = \frac{1}{2}mv^2} }$

Ek = Kinetic Energy ( Joule )

m = mass of the object ( kg )

v = speed of the object ( m/s )

Let us now tackle the problem !

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Given:

initial speed of the object = v

final speed of the object = ¹/₂v

Asked:

ratio of kinetic energy = Ek : Ek' = ?

Solution:

$Ek : Ek' = \frac{1}{2}mv^2 : \frac{1}{2}m(v')^2$

$Ek : Ek' = v^2 : (v')^2$

$Ek : Ek' = v^2 : (\frac{1}{2}v)^2$

$Ek : Ek' = v^2 : \frac{1}{4}v^2$

$Ek : Ek' = 1 : \frac{1}{4}$

$Ek : Ek' = 4 : 1$

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Learn more

• Impacts of Gravity : https://brainly.com/question/5330244
• Effect of Earth’s Gravity on Objects : https://brainly.com/question/8844454
• The Acceleration Due To Gravity : https://brainly.com/question/4189441
• Newton's Law of Motion: https://brainly.com/question/10431582
• Example of Newton's Law: https://brainly.com/question/498822

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Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics

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Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant , Wall