A projectile is fired vertically upwards with an initial velocity u . After an interval of T seconds a second projectile is fired vertically upwards, also with initial velocity u .
Text Solution
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For first projectile, \(h_{1} = ut - \frac{1}{2}gt^{2}\)
For second projectile, \(h_2 = u(t - T) - \frac{1}{2} g (t - T)^2\)
When both meet i.e. h_1 = h_2
\(ut - \frac{1}{2}gt^{2} = u(t - T) - \frac{1}{2}g(t - T)^{2}\)
⇒ ⇒ \(uT + \frac{1}{2} gT^{2} = gtT\)
⇒ ⇒ \(t = \frac{u}{g} + \frac{T}{2}\)
and \(h_1 = u \left( \frac{u}{g} + \frac{T}{2} \right) - \frac{1}{2} g \left( \frac{u}{g} + \frac{T}{2} \right)^2\)
\(= \frac{u^{2}}{2g} - \frac{gT^{2}}{8}\) .
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