A girl in a swing is 2.5 m above ground at the maximum height and at 1.5 m above the ground at the lowest point. Her maximum velocity in the swing is `(g = 10 ms^(-2)) `

Options

A. `5sqrt(2) ms^(-1)`
B. `2sqrt(5) ms^(-1)`
C. `2sqrt(3) ms^(-1)`
D. `3sqrt(2) ms^(-1)`

Answer

B

Explanation

At the highest point, `v = 0, h_1 = 2.5 m`
`:.` Total energy `, E_1 = mgh_1 + 0 = mgh_1`
At the lowest point, `v = ?, h_2 = 1.5 m`
`:. ` Total energy , `E_2 = mgh_2 + 1/2 mv^2`
According to the law of conservation of mechanical energy
`E_1 = E_2`
`:. mgh_1 = 1/2 mv^2 + mgh_2 " or " v^2 = 2g (h_1 - h_2)`
Or `v = sqrt(2h(h_1 - h_2)) = sqrt(2 xx 10 xx (2.5 - 1.5)) = 2sqrt(5) ms^(-1)`.