Question

At her maximum height, a girl in a swing is 3 m above the ground and at the lowest point, she is 2 m above the ground. What is her maximum velocity?

• A. $\sqrt{19.6}m{s}^{-1}$
• B. $\sqrt{39.2}m{s}^{-1}$
• C. $\sqrt{9.8}m{s}^{-1}$
• D. $9.8m{s}^{-1}$

Answer 1

Answer: (A)

At the highest point, $v=0,h_1=3m$
$\therefore$ Total energy, $E_1=mg{h}_1+0$
At the lowest point, $v=?,h_2=2m$
Total energy, $E_2=mg{h}_2+\frac{1}{2}m{\upsilon }^2$
According to the law of conservation of energy, $E_2=E_1$
$mg{h}_2+\frac{1}{2}m{\upsilon }^2=mg{h}_1$
$\upsilon =\sqrt{2g\left(h_2-h_1\right)}$
$=\sqrt{2\times 9.8\left(3-2\right)}$
$\upsilon =\sqrt{19.6}m{s}^{-1}$