A ball is projected upwards from the top of tower with a velocity \(50 \, ms^{-1}\) making an angle 30^\circ with the horizontal. The height of tower is 70 m . After how many seconds from the instant of throwing will the ball reach the ground
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The vertical component of velocity of projection \(= -50 \sin 30^\circ = -25 \, m/s\)
If t be the time taken to reach the ground,
\(h = ut + \frac{1}{2}gt^{2}\) ⇒ ⇒ \(70 = -25t + \frac{1}{2} \times 10 t^{2}\)
⇒ ⇒ 70 = -25t + 5t^{2} ⇒ ⇒ t^{2} - 5t - 14 = 0 ⇒ ⇒ t = – 2 s and 7 s
Since, t = – 2 s is not valid ∴ ∴ t = 7 s
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