Question

A ball when thrown vertically upwards reaches a maximum height of 19.3m. Find the velocity with which this ball was thrown to reach this height and the time taken by it

Answer 1

Answer:

Given:

Max height reached = 19.3 m

To find:

Initial velocity of Projection and the time taken to reach that height.

Concept:

Acceleration is considered to be constant and equal to 9.8 m/s² (i.e. gravitational acceleration). Since the acceleration is constant, we can use the equations of Kinematics.

Calculation:

${v}^{2} = {u}^{2} + 2( - g)h$

$= > {0}^{2} = {u}^{2} + 2( - 9.8)(19.3)$

$= > {u}^{2} = 378.28$

$= > u = 19.44 \: m {s}^{ - 1}$

Let time taken be t

$v = u + at$

$= > 0 = 19.44 + ( - 9.8)t$

$= > t = \dfrac{19.44}{9.8}$

$= > t = 1.98 \: sec$

Answer 2

AnSwEr :

$\mathfrak{Given} \begin{cases} \sf{Final\: velocity \: (v) \: = \: 0 \: ms^{-1}} \\ \sf{Distance \: or \: Height \: (s) \: = \: 19.3 \: m} \\ \sf{Acceleration \: = \: - \: 9.8 \: ms^{-2}}\end{cases}$

$\bigstar {\underline{\sf{We \: have \: to \: find \: Time \: and \: velocity}}}$

$\footnotesize {\underline{\sf{\dag \: \: \: \: \: \: \: \: Use \: 3rd \: equation \: of \: motion \: \: \: \: \: \: \:}}} \\ \\ \dashrightarrow \tt{v^2 \: - \: u^2 \: = \: 2gs}$

$\dashrightarrow \tt{0^2 \: - \: u^2 \: = \: 2 \: \times \: -9.8 \: \times \: 19.3} \\ \\ \dashrightarrow \tt{-u^2 \: = \: -378.28}$

$\dashrightarrow \tt{u^2 \: = \: 378.28}$

$\dashrightarrow \tt{u \: = \: \sqrt{378.28}}$

$\dashrightarrow \tt{u \: = \: 19.44}$

$\underline{\boxed{\sf{Initial \: velocity \: is \: 19.44 \: ms^{-1}}}}$

$\rule{150}{1}$

$\footnotesize {\underline{\sf{\dag \: \: \: \: \: \: Use \: 1st \: Equation \: of \: motion \: \: \: \: \:}}}$

$\dashrightarrow \tt{v \: = \: u \: + \: gt}$

$\dashrightarrow \tt{0 \: = \: 19.44 \: + \: (-9.8) \: \times \: t}$

$\dashrightarrow \tt{-19.44 \: = \: -9.8t}$

$\dashrightarrow \tt{19.44 \: = \: 9.8t}$

$\dashrightarrow \tt{t \: = \: \dfrac{19.44}{9.8}}$

$\dashrightarrow \tt{t \: = \: 1.98}$

$\underline{\boxed{\sf{Time \: Taken \: is \: 2 \: s}}}$