Question

A stone is thrown from a point A at the top of a building of height H = 14 m with an initial downward velocity v - -2m/s. What is the time needed for this stone to reach a point B at a height h = 4 m above the ground? Neglect the effect of air resistance, and use g = 10 m/s

Answer 1

Given

Total height of the building, H=14 m

The initial velocity is v=-2 m/s

The point B is at height, h=4 m.

To find

The time need by the stone to reach point B.

Explanation

Using the equation of kinematics,

$y=ut+\frac{1}{2}gt^2$

where y is the distance covered.

t is the time taken

Thus,

$\begin{gathered} H-h=vt+\frac{1}{2}gt^2 \\ \Rightarrow14-4=2t+\frac{1}{2}\times10\times t^2 \\ \Rightarrow10=5t^2+2t \\ \Rightarrow5t^2+2t-10=0 \\ \Rightarrow t=\frac{-2\pm\sqrt{4+200}}{10} \\ \Rightarrow t=1.28\text{ s \lparen considering only the positive term\rparen} \end{gathered}$

Conclusion

The time is 1.28 s