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Manish Dass
Asked: 2022-11-11T06:18:01+05:30 In:

A running man has half the KE that a body of half his mass has. The man speeds up by `1.0ms^(-1)` and then has the same energy as the boy. What were the original speeds of the man and the boy?
A. `(sqrt2+1),(sqrt2-1)`
B. `(sqrt2+1),2(sqrt2+1)`
C. `sqrt2,sqrt2`
D. `(sqrt2+1),2(sqrt2-1)`

A running man has half the KE that a body of half his mass has. The man speeds up by `1.0ms^(-1)` and then has the same energy as the boy. What were the original speeds of the man and the boy?
A. `(sqrt2+1),(sqrt2-1)`
B. `(sqrt2+1),2(sqrt2+1)`
C. `sqrt2,sqrt2`
D. `(sqrt2+1),2(sqrt2-1)`
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  1. Correct Answer – B
    (b) According to the question, `(1)/(2) mv_(1)^(2)=(1)/(2)[(1)/(2)xx(m)/(2)xxv_(2)^(2)]`
    where, `v_(1)=”speed of man and “v_(2)`=speed of boy
    Now, `(1)/(2)m(v_(1)+1)^(2)=(1)/(2)xx(m)/(2)xxv_(2)^(2)`
    Solving these two equations we get, `v_(1)=(sqrt2+1)ms^(-1)` and `v_(2)=2(sqrt2+1)ms^(-1)`

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Binoya Brar
Asked: 2022-11-05T04:30:42+05:30 In:

A running man has half the KE that a body of half his mass has. The man speeds up by `1.0ms^(-1)` and then has the same energy as the boy. What were the original speeds of the man and the boy?
A. `sqrt(2)m//s`
B. `(sqrt(2)-1)m//s`
C. `(1)/((sqrt(2)-1))m//s`
D. `(1)/(sqrt(2))m//s`

A running man has half the KE that a body of half his mass has. The man speeds up by `1.0ms^(-1)` and then has the same energy as the boy. What were the original speeds of the man and the boy?
A. `sqrt(2)m//s`
B. `(sqrt(2)-1)m//s`
C. `(1)/((sqrt(2)-1))m//s`
D. `(1)/(sqrt(2))m//s`
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  1. Correct Answer – C

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Ganesh Sachdeva
Asked: 2022-11-03T16:55:44+05:30 In:

A running man has half the KE that a body of half his mass has. The man speeds up by `1.0ms^(-1)` and then has the same energy as the boy. What were the original speeds of the man and the boy?
A. `2.4, 4.8 ms^(-1)`
B. `2.4, 3.4 ms^(-1)`
C. `3.4, 4.8 ms^(-1)`
D. `3.4, 6.8 ms^(-1)`

A running man has half the KE that a body of half his mass has. The man speeds up by `1.0ms^(-1)` and then has the same energy as the boy. What were the original speeds of the man and the boy?
A. `2.4, 4.8 ms^(-1)`
B. `2.4, 3.4 ms^(-1)`
C. `3.4, 4.8 ms^(-1)`
D. `3.4, 6.8 ms^(-1)`
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  1. Let M = mass of man , m= mass of boy V = speed of man , v = speed of boy
    Given `(1)/(2) MV^(2) = (1)/(2) ((1)/(2)mv^(2))`, As `m = (M)/(2)`
    So `(1)/(2) MV^(2) = (1)/(2) ((1)/(2) xx (M)/(2) mv^(2))`
    Hence `v^(2) = 4V^(2)` or `v = 2V`
    When the man speeds up by `1 m//s`, then we get
    `(1)/(2) M (V + 1)^(2) = (1)/(2)mv^(2) = (1)/(2) (M)/(2) (4V^(2))`
    or `(V + 1)^(2) = 2V^(2)` or `V^(2) – 2V – 1 = 0`
    Solving we get `V = 2.4 ms^(-1)` and` v = 2V = 4.8 ms^(-1)`

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