Question

A boy is sitting on a swing at a maximum height of $5$m above the ground. When the swing passes through the mean position which is $2$m above the ground, its velocity is approximately:

• A. $7.6$ m/s
• B. $9.8$ m/s
• C. $6.26$ m/s
• D. None of these

Answer 1

Answer: (A)

$7.6$ m/s

The law of conservation of energy states that the total amount of
energy in
an isolated system remains constant over time.
At a maximum height:

$K_0=0$

$P_0=m\times g\times H$

$K_1=m\times \frac{V^2}{2}$

$P_1=m\times g\times h$

$K_0+P_0=K_1+P_1$

$m\times g\times H=m\times \frac{V^2}{2}+m\times ghg\times H$

$=\frac{V^2}{2}+g\times h$

$\frac{V^2}{2}=g\times H-g\times h$

$V=\sqrt{(2\times g\times (H-h\left)\right)}$

$V=\sqrt{(2\times 9.81\times (5-2\left)\right)}=7.67\frac{m}{s}$