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Question
In a shotput event an athlete throws the shotput of mass 10 kg with an initial speed of 1 ms–1 at 45° from a height 1.5 m above ground. Assuming air resistance to be negligible and acceleration due to gravity to be 10 ms–2, the kinetic energy of the shotput when it just reaches the ground will be ______.
Options
2.5 J
5.0 J
52.5 J
155.0 J
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Solution
In a shotput event an athlete throws the shotput of mass 10 kg with an initial speed of 1 ms–1 at 45° from a height 1.5 m above ground. Assuming air resistance to be negligible and acceleration due to gravity to be 10 ms–2, the kinetic energy of the shotput when it just reaches the ground will be 155.0 J.
Explanation:
If air resistance is negligible, the total mechanical energy of the system will remain constant. And let us take the ground as a reference where potential energy will be zero.
According to the problem, h = 1.5 m, v = 1 m/s, m = 10 kg, g = 10 ms– 2
The initial energy of the shotput = `(PE)_i + (KE)_i`
= `mgh + 1/2 mv^2`
= `10 xx 10 xx 1.5 + 1/2 xx 10 xx (1)^2`
= 150 + 5
= 155 J
From the conservation of mechanical energy,
`(PE)_i + (KE)_i = (PE)_f + (KE)_f`
⇒ `155_j = 0 + (KE)_f`
So, the final kinetic energy of the shotput is 155 J.
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