A balloon rising vertically up with uniform velocity 15 ms^-1 , releases a ball at a height of 100 m . Calculate the time taken by the ball to hit the ground .Explain clearly .(g=10ms^-2).

Taking vertically upward direction to be positive
Initial velocity of the ball(u) = -15 m/s
Displacement of the ball(S) = 100 m
Acceleration = g = 10 m/s²
Let the time taken by the ball to reach the ground be t
Applying $S=ut+\frac{1}{2}a{t}^2$
$$\begin{gathered} 100=-15t+\frac{1}{2}10\times t^2 \\ \mathrm{or}, 20=-3t+t^2 \\ {t}^2-3t-20=0 \\ t=\frac{3\pm \sqrt{9-4(-20)}}{2}=\frac{3\pm \sqrt{89}}{2} \\ t=\frac{3+\sqrt{89}}{2}=6.21 \sec \end{gathered}$$