Question : A child is sitting on a swing. Its minimum and maximum heights from the ground 0.75 m and 2 m respectively' it's maximum speed will be
(a) 10m/s
(b) 5 m/s
(c) 8 m/s
(d) 15m/s
Doubt by Ishmeet
Solution :
h1=0.75 m
h2=2 m
As per the law of conservation of energy
As per the law of conservation of energy
KE=PE
½mv²=mg(h2-h1)
½v²=g(h2-h1)
v²=2g(h2-h1)
v²=2(9.8)[2-0.75]
v²=2(9.8)[1.25]
½mv²=mg(h2-h1)
½v²=g(h2-h1)
v²=2g(h2-h1)
v²=2(9.8)[2-0.75]
v²=2(9.8)[1.25]
v²=9.8×2.50
v²=4.9×2×2.50
v²=4.9×5
v²=(49/10)×5
v²=49/2
v=√[49/2]
v=7/√2
v=7×0.707 [∵1/√2=0.707]
v=4.949
v≈5 m/s
v²=4.9×2×2.50
v²=4.9×5
v²=(49/10)×5
v²=49/2
v=√[49/2]
v=7/√2
v=7×0.707 [∵1/√2=0.707]
v=4.949
v≈5 m/s
Hence, (b) 5 m/s, would be the correct option.
Note : Although g=10 m/s² is not given in the question but if we have taken it then the calculations will be become quite easier. So in MCQs feel free to take g=10 m/s² and match it with the closest answer among the options.