Question

A ball thrown vertically upwards with speed 'u' from the top of a tower reaches the ground in $9$ s. Another ball is thrown vertically downwards from the same position with speed 'u'. take $4$ s to reach the ground. Calculate the value of 'u'. $(Takeg=10{ms}^{-2})$

• A. $15{ms}^{-1}$
• B. $20{ms}^{-1}$
• C. $25{ms}^{-1}$
• D. $45{ms}^{-1}$

Answer 1

The correct option is C $25{ms}^{-1}$

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

For the first case, velocity = $u$ , Time $t=9s$,

Using $s=ut+\frac{1}{2}a{t}^2$ $\Rightarrow -h=u\times 9-\frac{1}{2}\times 10\times 9^2$

$\Rightarrow -h=9u-405$ .....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,

$\Rightarrow 9u-405=-4u-80$ $\Rightarrow u=25m{s}^{-1}$