Question

A body is projected into the air with a velocity of 98 m/s at an angle of 30 degree to the horizontal. Its time of flight is

Answer 1

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✤ Required Answer:

✒GiveN:

• Initial velocity = 98 m/s
• Angle with horizontal = 30°

✒ To FinD:

• Time of flight of the projectile....?

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✤ How to solve?

Before solving this question, Let's know some basic concepts regarding Projectile motion,

• Projectile motion is the motion when an object is thrown at some angle with horizontal. It is allowed to move in two dimensions under the action lf gravity.
• The path of the projected body is also known as Trajectory.

Here, are some of the formulas used in this kind of motion for finding time of flight, Horizontal displacement, vertical height(max).

$\large{ \sf{ \cdot \: {t = \dfrac{2v_0 \sin( \theta) }{g} }}}$

$\large{ \sf{ \cdot \: {H = \dfrac{v_0 {}^{2} \sin {}^{2} ( \theta) }{2g} }}}$

$\large{ \sf{ \cdot \: {R = \dfrac{v_0 {}^{2} \sin2( \theta) }{g} }}}$

Here, H is the maximum height reached, R is the horizontal range and t is the time of flight.

By using these formulas, let's solve

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✤ Solution:

We have,

• $\sf{v_0 = 98 m/s}$
• Angle $\sf{\theta}$ = 30°

So, By using formula,

Considering g = 9.8 m/s²,

$\large{ \sf{ \longrightarrow \:t = \dfrac{2v_0 \sin( \theta) }{g} }}$

$\large{ \sf{ \longrightarrow \: t = \dfrac{2 \times 98 \times \sin(30 ) }{9.8} }}$

$\large{ \sf{ \longrightarrow \: t = \dfrac{2 \times 98 \times \frac{1}{2} }{9.8} \: s}}$

$\large{ \sf{ \longrightarrow \: t = 2 \times 10 \times \frac{1}{2} \: s }}$

$\large{ \sf{ \longrightarrow \: t = \boxed{ \sf{ \red{10 \: s}}}}}$

✒ Time of flight of the body = 10s

☀️ Hence, solved !!

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Answer 2

Given ,

Initial velocity (u) = 98 m/s

Angle of projection (Φ) = 30

We know that , the time of flight of body is given by

$\boxed{ \sf{T = \frac{2u \sin( \theta) }{g} }}$

Thus ,

$\sf \mapsto T = \frac{2 \times 98 \times \sin(30) }{9.8} \\ \\\sf \mapsto T = 2 \times 10 \times \frac{1}{2} \\ \\\sf \mapsto T = 10 \: \: sec$

$\sf\therefore \underline{ {The \: time \: of \: flight \: of \: a \: body \: is \: 10 \: sec}}$