Question

A ball which is thrown vertically up from the top of the tower reaches the ground in $12$ s. Another ball thrown vertically downwards from the same position with the same velocity takes $4$ s to reach the ground. Find the height of the tower. $(Takeg=10{ms}^{-2})$

• A. $180$ m
• B. $120$ m
• C. $220$ m
• D. $240$ m

Answer 1

The correct option is D $240$ m

Ball is thrown from the top of tower, $\Rightarrow height=-h$,

For the first case, velocity = $u$ , Time $t=12s$,

Using $s=ut+\frac{1}{2}a{t}^2$ $\Rightarrow -h=u\times 12-\frac{1}{2}\times 10\times {12}^2$

$\Rightarrow -h=12u-720$ .....1

For the second case, velocity = $-u$ , Time $t=4s$,

Using $s=ut+\frac{1}{2}a{t}^2$ $\Rightarrow -h=-u\times 4-\frac{1}{2}\times 10\times 4^2$

$\Rightarrow -h=-4u-80$ .....2

Equating equations 1 and 2,

$\Rightarrow 12u-720=-4u-80$ $\Rightarrow u=40m{s}^{-1}$

Put the value of $u=40m{s}^{-1}$ in equation 1,

$\Rightarrow -h=12\times 40-720$ $\Rightarrow h=240m$