Question

A 60 kg runner in a sprint moves at 11 m/s. A 60 kg cheetah in a sprint moves at 33 m/s. By what factor does the kinetic energy of the cheetah exceed that of the human runner?

Answer 1

The kinetic energy of the cheetah exceed by the 9 times of the runner.

Step-by-step explanation:

Given that,

Mass of runner = 60 kg

Velocity of runner = 11 m/s

Mass of cheetah = 60 kg

Velocity of cheetah = 33 m/s

We need to calculate the kinetic energy of the cheetah

Using formula of kinetic energy

`K.E=(1)/(2)mv^2`

Kinetic energy of runner

`K.E_(r)=(1)/(2)m_(r)v_(r)^2`....(I)

Kinetic energy of cheetah

`K.E_(c)=(1)/(2)m_(c)v_(c)^2`....(II)

From equation (I) and (II)

`(K.E_(r))/(K.E_(c))=((1)/(2)m_(r)v_(r)^2)/((1)/(2)m_(c)v_(c)^2)`

`K.E_(c)=((1)/(2)m_(c)v_(c)^2)/((1)/(2)m_(r)v_(r)^2)*K.E_(r)`

Put the value into the formula

`K.E_(c)=((1)/(2)*60*(33)^2)/((1)/(2)*60*(11)^2)*K.E_(r)`

`K.E_(c)=9K.E_(r)`

Hence, The kinetic energy of the cheetah exceed by the 9 times of the runner.

Answer 2

Step-by-step explanation:

It is given that,

Mass of the runner, m₁ = 60 kg

Speed of runner, v₁ = 11 m/s

Mass of cheetah, m₂ = 60 kg

Speed of cheetah, v₂ = 33 m/s

Kinetic energy of runner,
`E_r=(1)/(2)m_1v_1^2`

`E_r=(1)/(2)* 60* (11)^2=3630`........(1)

Kinetic energy of cheetah,
`E_c=(1)/(2)m_2v_2^2`

`E_c=(1)/(2)* 60* (33)^2=32670\ J`..............(2)

From equation (1) and (2), it is clear that

`E_c= 9* E_r`

So, the kinetic energy of the cheetah is nine times that of human runner. Hence, this is the required solution.