Question

A projectile is fired with initial velocity of 100m\s at an angle of 30° with the horizontal calculate the maximum height attained

Answer 1

Answer:

• 125 metres is the maximum height attained .

Explanation:

According to the Question

It is given that ,

• Initial velocity ,u = 100m/s
• Angle of Projection ,θ = 30°
• Acceleration due to gravity ,g = 10m/s²

$\bigstar\boxed{\bf{H_{max} = \frac{u^{2}Sin^{2}\theta}{2g}}}$

$\sf\dashrightarrow\; H_{max} = \frac{100^{2} Sin^{2}30^{\circ}}{2\times10} \\\\\sf\dashrightarrow\; H_{max} = \frac{10000 \times (\frac{1}{2})^{2} }{20} \\\\\sf\dashrightarrow\; H_{max} = \frac{10000 \times (\frac{1}{4})}{20} \\\\\sf\dashrightarrow\; H_{max} =\frac{500}{4} \\\\\sf\dashrightarrow\; H_{max} = 125 \\\\\boxed{\bf{Hence, the \; maximum \; height \; attained\; is \; 125 \;metres.}}$

Answer 2

Answer:

Given :

• A projectile is fired with initial velocity of 100 m/s at an angle of 30° with the horizontal.

To Find :-

• What is the maximum height attained.

Formula Used :-

$\clubsuit$ Maximum Height Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Maximum\: Height =\: \dfrac{v^2sin^2\theta}{2g}}}}\: \: \: \bigstar$

where,

• v = Velocity
• g = Acceleration due to gravity

Solution :-

Given :

• Velocity = 100 m/s
• Acceleration due to gravity = 9.8 m/s²
• Angle of projection = 30°

According to the question by using the formula we get,

$\implies \bf Maximum\: Height =\: \dfrac{v^2sin^2\theta}{2g}$

$\implies \sf Maximum\: Height =\: \dfrac{(100)^2 \times sin^2\: 30^{\circ}}{2(9.8)}$

As we know that :

$\diamond \: \: \sf\bold{\pink{sin\: 30^{\circ} =\: \dfrac{1}{2}}}$

$\implies \sf Maximum\: Height =\: \dfrac{(100 \times 100) \times \bigg(\dfrac{1}{2}\bigg)^2}{2 \times 9.8}$

$\implies \sf Maximum\: Height =\: \dfrac{\cancel{10000} \times \dfrac{1}{\cancel{4}}}{19.6}$

$\implies \sf Maximum\: Height =\: \dfrac{2500}{19.6}$

$\implies \sf\bold{\red{Maximum\: Height =\: 127.55\: metres}}$

$\therefore$ The maximum height attained is 127.55 metes .

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EXTRA IMPORTANT FORMULA :-

$\clubsuit$ Horizontal Range Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Horizontal\: Range(R) =\: \dfrac{v^2sin2\theta}{g}}}}\: \: \: \bigstar$

$\clubsuit$ Time Taken Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Time\: Taken (t) =\: \dfrac{2vsin\theta}{g}}}}\: \: \: \bigstar$

where,

• v = Velocity
• g = Acceleration due to gravity