Respuesta :
Answer:
The difference in speed of the dog and cat is 2.65 m/s
Explanation:
Given that,
Mass of cat = 0.45 times the mass of dog
K.E of dog = 0.55 times K.E of cat
We need to calculate the velocity of dog
Using given data
[tex]\dfrac{1}{2}m_{d}v_{d}^2=0.55\times\dfrac{1}{2}m_{c}v_{c}^2[/tex]
[tex]m_{d}v_{d}^2=0.55\times0.45\times m_{d}\times v_{c}^2[/tex]
[tex]v_{d}^2=0.2475\times v_{c}^2[/tex]
[tex]v_{d}=0.497v_{c}[/tex]....(I)
The dog speeds up by 0.91 m/s and then has the same kinetic energy as the cat.
We need to calculate the velocity of dog
Using conservation of kinetic energy,
[tex]\dfrac{1}{2}m_{d}v_{d}^2=\dfrac{1}{2}m_{c}v_{c}^2[/tex]
[tex]\dfrac{1}{2}m_{d}(v_{d}+0.91)^2=\dfrac{1}{2}m_{c}v_{c}^2[/tex]
[tex]m_{d}(v_{d}+0.91)^2=0.45m_{d}v_{c}^2[/tex]
[tex]v_{d}+0.91=0.67v_{c}[/tex]
[tex]v_{d}=0.67v_{c}-0.91[/tex]...(II)
From equation (I) and (II)
[tex]0.497v_{c}=0.67v_{c}-0.91[/tex]
[tex]v_{c}=\dfrac{-0.91}{(0.497-0.67)}[/tex]
[tex]v_{c}=5.26\ m/s[/tex]
Put the value in equation (I)
[tex]v_{d}=0.497\times5.26[/tex]
[tex]v_{d}=2.61\ m/s[/tex]
We need to calculate the difference in speed of the dog and cat
Using speed of dog and cat
[tex]v_{c}-v_{d}=5.26-2.61[/tex]
[tex]v_{c}-v_{d}=2.65\ m/s[/tex]
Hence, The difference in speed of the dog and cat is 2.65 m/s
