A 15 g ball is shot from a spring gun whose spring has a force constant of 600 N/m. The spring is compressed by 5 cm. The greatest possible horizontal range of the ball for this compression is (g = 10 m/s 2 )
Text Solution
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For getting horizontal range, there must be some inclination of spring with ground to project ball.
⇒ ⇒ $R_{\max} = \frac{u^{2}}{g}$ …..(i)
But K.E. acquired by ball = P.E. of spring gun
$\frac{1}{2}mu^{2} = \frac{1}{2}kx^{2} \Rightarrow u^{2} = \frac{kx^{2}}{m}$ …..(ii)
From equation (i) and (ii)
$R_{\max} = \frac{kx^2}{mg} = \frac{600 \times (5 \times 10^{-2})^2}{15 \times 10^{-3} \times 10}$ =10m.
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