Question

An object is oblique shot into the air with a velocity of 30m/s at an angle 60degree calculate the time of flight of the object in air.(g=10m/s)

Answer 1

Given :

▪ Initial velocity = 30mps

▪ Angle of projection = 60°

▪ Acc. due to gravity = 10m/s²

To Find :

▪ Time of flight

SoluTion :

↗ For a projectile fired with velocity u at an angle Φ with the horizontal,

✴ Time of flight (T) :-

$\bigstar\:\underline{\boxed{\bf{\purple{T=\dfrac{2u\sin\phi}{g}}}}}$

• T denotes time of flight
• u denotes initial velocity
• Φ denotes angle of projection
• g denotes acc. due to gravity

$\green{\dashrightarrow}\tt\:T=\dfrac{2u\sin\phi}{g}\\ \\ \green{\dashrightarrow}\tt\:T=\dfrac{2\times 30\times \sin60\degree}{10}\\ \\ \green{\dashrightarrow}\tt\:T=\dfrac{6\times \sqrt{3}}{2}\\ \\ \green{\dashrightarrow}\tt\:T=3\sqrt{3}\\ \\ \green{\dashrightarrow}\underline{\boxed{\bf{\pink{T=5.19s}}}}\:\orange{\bigstar}$

⚽ Learn more :

• A body is said to be projectile if it is projected into space with some initial velocity and then it continues to move in a vertical plane such that its horizontal acc. is zero and vertical downward acc. is equal to g.
• In projectile motion, the horizontal and the vertical motion are independant of each other.
• The horizontal range is same when the angle of projection is Φ and (90°- Φ).
• At the highest point of the parabolic path, the velocity and acceleration of a projectile are perpendicular to each other.

Answer 2

$\bold{\bf{\red{T=\frac{2usin\theta}{g}}}}$

where ,

• T denotes time of flight
• u denotes initial velocity
• Ф denotes angle of projection
• g denotes gravity

Given ,

Initial velocity , u = 30 m/s

Angle of projection , Ф = 60⁰

Gravity , g = 10 m/s²

Now sub. values in formula we will get time of flight

$\bold{T=\frac{2(30)(sin60)}{10} }\\\\\bold{T=\frac{30\sqrt{3}}{10} }\\\\\bold{T=3\sqrt{3}}\\\\\bold{\bf{\red{T=5.19\;sec}}}$

So the time of flight of the object in air is 5.19 seconds.