Question

A ball is throw at an angle of 30 degrees off the horizontal, with an initial velocity of 28 m/s. what is the maximum height the ball will reach?

Answer 1

Given:

Angle of projection, $\theta$ = $30^{\circ}$

Initial velocity of projectile, u = 28 $ms^{-1}$

To find:

Maximum height reached by the projectile, H =?

Formula required:

Formula to calculate the maximum height 'H' reached by a projectile with angle of projection $\theta$, and initial velocity of projectile 'u', and acceleration due to gravity 'g'.

$\bigstar \;\;\;\;\;H=\dfrac{u^2\;sin^2\theta}{2\;g}$

Solution:

Using formula to calculate the Maximum hight reached by projectile

$\to \; H = \dfrac{u^2\;sin^2\theta}{2\;g}$

$\to\;H = \dfrac{(28)^2\;sin^2 30^{\circ}}{2\;(9.8)}$

$\to\;H = \dfrac{784 \times \;sin^230^{\circ}}{19.6}$

$\to\;H = \dfrac{784}{19.6}\times sin^2 30^{\circ}$

$\to\;H = \dfrac{784}{19.6}\times \bigg(\dfrac{1}{2}\bigg)^2$

$\to\;H = \dfrac{784}{19.6}\times \dfrac{1}{4}$

$\to\;\;\boxed{\boxed{H=10\;\;m}}$

Therefore,

The maximum height reached by the projectile will be 10 metres.

Answer 2

Explanation:

Given :

• A ball is throw at an angle = 30°

• Initial velocity of projectile = 28

To find :

• what is the maximum height the ball will reach?

Solution :

$\sf : \implies \: \: \: \: \: \: \: \: \: \: H = \dfrac{u^2\;sin^2\theta}{2\;g}$

Substitute all values :

$\sf : \implies \: \: \: \: \: \: \: \: \: \: H = \dfrac{(28)^2\;sin^2 30^{\circ}}{2\;(9.8)}$

$\sf : \implies \: \: \: \: \: \: \: \: \: \: \: H = \dfrac{ \cancel{784 }\times \;sin^230^{\circ}}{ \cancel{19.6} }\\ \\ \\ \sf : \implies \: \: \: \: \: \: \: \: \: \: \: H = 4 0 \times {\bigg( \: \: \frac{1}{2} \: \bigg)}^{2} \: \\ \\ \\ \sf : \implies \: \: \: \: \: \: \: \: \: \: \: H = \cancel{40 }\times \bigg( \: \: \frac{1}{ \cancel{4}} \: \bigg) \\ \\ \\ \sf : \implies \: \: \: \: \: \: \: \: \: \: \: H = 10$

⠀

$\therefore\:\underline{\textsf{Hence, the required answer is \textbf{10}}}.$

$\rule{180}{1.5}$

$\bigstar\:\sf Trigonometric\:Values :\\\begin{tabular}{|c|c|c|c|c|c|}\cline{1-6}Radians/Angle & 0 & 30 & 45 & 60 & 90\\\cline{1-6}Sin \theta & 0 & \dfrac{1}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{\sqrt{3}}{2} & 1\\\cline{1-6}Cos \theta & 1 & \dfrac{\sqrt{3}}{2}& \dfrac{1}{\sqrt{2}}& \dfrac{1}{2}&0\\\cline{1-6}Tan \theta&0& \dfrac{1}{\sqrt{3}}&1&\sqrt{3}& Not D \hat{e} fined \\\cline{1-6}\end{tabular}$