# Time of Flight Formula, Calculation, Example – Projectile Motion

### Time of Flight Calculator – Projectile Motion

Time of flight calculator, you can easily calculate the time the projectile stays in the air. To solve this special case of projectile motion, all you need to enter is the initial velocity, angle, and height.

Time of Flight Calculator – Projectile Motion formula is given by,

When the object is launch from the ground (initial height h = 0)

Time of flight t = 2 * V * sin (α) / g

When the object is launch from some height (initial height > 0)

Time of flight t = [V * sin (α) +√(( V * sin (α))2 + 2 * g * h )] /g

Where ,

V is the initial velocity

α is the angle of launch

h is the initial height

t is the time of flight

### Example 1:

A body is rejected with a velocity of  10 m/s at 600  to the horizontal  plane and from a height of 4m. find the time of flight of the projectile?

### Solution :

Initial velocity V = 10 m/s

Angle of launch α = 60

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Initial height h = 4m

Acceleration due to gravity g = 9.8

Sin(60) = 0.866

Time of flight formula is

T = [V * sin (α) +√(( V * sin (α))2 + 2 * g *h)]/g

= [10 *sin (60) + √((10 * sin (60))2 + 2 * 9.8 * 4)] / 9.8

= [10 * 0.866 +  √((10 * 0.866))2 + 78.4)] /9.8

= [8.66+  √(( 8.66)2+78.4)]/9.8

= [8.66+  √(74.99+78.4)]/9.8

=   [8.66+  √(153.39)] /9.8

=   [8.66+ 12.38 ]/9.8

= 21.04 /9.8

= 2.14

There the time of flight of projectile is 2.14 seconds.

### Example 2:

A body projected with an initial velocity of 15 m/s at 35 to the horizontal plane. Find the time of flight of the projectile.

### Solution :

Initital velocity V = 15 m/s

Angle of launch α = 35

Time of flight is t = 2* 15 * sin(35) /9.8

T = 30 *0.573 /9.8

=17.19 /9.8

= 1.75 seconds.

So the time of  flight is 1.75 seconds.