Question

While sitting on top of a 10m building you drop a chestnut,when it reaches a height of 2.5m you droo another chestnut.What initial speed should you give the second chestnut if they're both to reach at the same time?

Answer 1

$h=v^2/(2g)\to v=\sqrt{2gh}=\sqrt{2\cdot9.81\cdot(10-2.5)}=12.13(m/s)$

$2.5=vt+gt^2/2\to 4.905t^2+12.13t-2.5=0\to$

$t=0.191(s)$

So,

$10=ut+gt^2/2\to u=\frac{10-gt^2/2}{t}=\frac{10-9.81 \cdot 0.191^2/2}{0.191}=51.42(m/s )$. Answer