Question

10. The kinetic energy of a man is half the kinetic energy of a boy of half of his mass. If the man inores
his speed by Ims, then his kinetic energy becomes equal to that of the boy. The velocity the man is​

Answer 1

Answer:

⚽ Correct Question :

▪ A running man has half the kinetic energy than a boy of half his mass has. The man speed up by 1mps and then he has the same energy as the boy. The original speeds of the man and boy respectively are ?

⚽ Solution :

• Mass of boy = m
• Mass of man = M
• Initial speed of boy = v
• Initial speed of man = V

→ As the kinetic energy of the man is half the kinetic energy of the boy

$\dashrightarrow\sf\:\dfrac{1}{2}MV^2=\dfrac{1}{2}{\huge(}\dfrac{1}{2}mv^2{\huge)}\\ \\ \dashrightarrow\sf\:\dfrac{1}{2}MV^2=\dfrac{1}{4}{\huge(}\dfrac{M}{2}{\huge)}v^2\longrightarrow\:\because\:m=\dfrac{M}{2}\\ \\ \dashrightarrow\sf\:v^2=4V^2\\ \\ \dashrightarrow\underline{\underline{\bf{v=2V}}}$

→ Now when the velocity of the man is increased to (V+1), then kinetic energies become equal

$\dashrightarrow\sf\:\dfrac{1}{2}M(V+1)^2=\dfrac{1}{4}M(2V)^2\\ \\ \dashrightarrow\sf\:V^2+2V+1=2V^2\\ \\ \dashrightarrow\sf\:V^2-2V-1=0\\ \\ \dashrightarrow\sf\:V=\sqrt{2}+1\\ \\ \dashrightarrow\underline{\boxed{\bf{\blue{V=2.4mps}}}}\:\gray{\bigstar}\\ \\ \dashrightarrow\sf\:v=2(\sqrt{2}+1)\\ \\ \dashrightarrow\underline{\boxed{\bf{\green{v=4.8mps}}}}\:\orange{\bigstar}$

Answer 2

Correct Question

A running man has half the kinetic energy than a boy of half his mass has. The man speed up by 1 m/s and then he has the same energy as the boy. The original speed of the man and boy respectively are ?

Answer

• Let the mass of boy be " m "
• Mass of the man be " M "
• Velocity of the boy be " v "
• Velocity of the man be " V "

A/c "  A running man has half the kinetic energy than a boy of half his mass has "

Here , M = m/2

$\implies \bold{\frac{1}{2}\;MV^2 =\frac{1}{2} (\frac{1}{2}\;mv^2 )}\\\\\implies \bold{\frac{1}{2}\;MV^2 =\frac{1}{4}\;\frac{M}{2} v^2 }\\\\\implies \bold{v^2=4V^2}\\\\\implies \bold{v=2V}$

Now , The man speed up by 1 m/s and then he has the same energy as the boy . So

$\implies \bold{\frac{1}{2}M(V+1)^2=\frac{1}{2}mv^2 }\\\\\implies \bold{\frac{1}{2}M(V+1)^2=\frac{1}{2}(\frac{M}{2})(2V)^2}\\\\\implies \bold{(V+1)^2=2V^2}\\\\\implies \bold{2V^2-V^2-1-2V=0}\\\\\implies \bold{V^2-2V-1=0}\\\\\implies \bold{V=2.4\;m/s}$

So , Velocity of man , V = 2.4 m/s

Velocity of boy , v = 2V = 4.8 m/s