Answer:
The minimum initial velocity is 10.31 m/s.
Explanation:
Given that,
Length = 23.8 feet
We need to calculate the height of the limb from the sling
[tex]h=23.8-6=17.8\ feet[/tex]
Using conservation of energy theorem
[tex]M.E_{i}=M.E_{f}[/tex]
[tex]P.E_{i}+K.E_{i}=P.E_{f}+K.E_{f}[/tex]
[tex]0+\dfrac{1}{2}m(v_{f}^2-v_{i}^2)=mgh+0[/tex]
[tex]\dfrac{1}{2}m(v_{f}^2-v_{i}^2)=mgh[/tex]
At position of limb, final velocity is zero.
[tex]v_{f}=0[/tex]
Put the value into the formula
[tex]\dfrac{1}{2}v_{i}^2=gh[/tex]
[tex]v_{i}=\sqrt{2gh}[/tex]
Put the value into the formula
[tex]v_{i}=\sqrt{2\times9.8\times5.42544}[/tex]
[tex]v_{i}=10.31\ m/s[/tex]
Hence, The minimum initial velocity is 10.31 m/s.
