Question

 If body is projected at an angle 30⁰ with horizontal with velocity 440 cm/s the time flight is -----

a) 0.4 sec     b) 0.550 sec    
  c) 0.448 sec      d) 0.5 sec​

Answer 1

Answer :-

Time of flight of the body is 0.448 sec . [Option.c]

Explanation :-

We have :-

→ Velocity of projection = 440 cm/s

→ Angle of projection = 30°

→ Acceleration due to gravity = 9.8 m/s²

→ sin 30° = 0.5

______________________________

Firstly let's convert the unit of velocity of projection from cm/s to m/s .

⇒ 1 cm/s = 0.01 m/s

⇒ 440 cm/s = 440(0.01)

⇒ 4.4 m/s

From formula for 'Time of Flight' of a projectile' :-

T = 2usinθ/g

Where :-

• T is the time period.

• u is the velocity of projection.

• θ is the angle of projection.

• g is acceleration due to gravity.

Substituting values, we get :-

⇒ T = (2 × 4.4 × 0.5)/9.8

⇒ T = 4.4/9.8

⇒ T = 0.448 sec

Answer 2

Given :-

If  body is projected at an angle 30⁰ with horizontal with velocity 440 cm/s

To Find :-

Time taken

Solution :-

We know that

100 cm/s = 1/1000 m/s

400 cm/s = 400 × 1/1000 = 4 × 1/10 = 4.4 m/s

Now

$\sf Time = \dfrac{2u\sin \theta}{g}$

$\sf Time = \dfrac{2\times 4.4 \times sin(30)^{\circ}}{9.8}$

$\sf Time = \dfrac{2 \times 4.4 \times \dfrac{1}{2}}{9.8}$

$\sf Time =\dfrac{8.8 \times \dfrac{1}{2}}{9.8}$

$\sf Time = \dfrac{4.4}{9.8}$

$\sf Time = 0.448 \; sec$