# Total Time of Flight

For an object which is launched from ground level, its movement can be represented by a parabolic shape. (fig.2.). The time required for the object to reach it’s maximum height is solely dependant on the initial vertical velocity of the object., and this can be calculated using v = u + at.

Fig. 2.

Clearly, for an object in parabolic motion, the initial velocity ‘u’ is the same as the initial vertical velocity ‘uv’ and the value for ‘a’ is - 9.8m/s2  (ie. This is negative because gravity is acting in the opposite direction as the object, as it reaches it’s maximum point). At the maximum point of motion, the final vertical velocity is always zero. That is,

0 = uv - 9.8 t
9.8 t = uv
Thus, t = uv / 9.8

The time which is required for the object to reach the ground again is also this same figure. Hence the total time, from the point of projection until it lands on the ground again is simply t = uv / 4.9

 t = uv / 4.8  or  t = usinx / 4.8 where,   t = total time of flight (secs)  uv = initial vertical velocity (m/s)  u = initial velocity of object (m/s)  x = angle of projection  (degrees)

## Examples

Q: Tang is launched with a velocity of 50m/s at 45 degrees to the ground. Assuming gravity is 9.8 m/s2, how much time will Tang spend in the air?

A:

Quoting from above:

>    0 = uv - 9.8 t
>    9.8 t = uv

Thus, total time of flight = t = uv / 4.9

Since total velocity = 50m/s, uv = 50 x sin 45

t = 50 x sin 45 / 4.9 = 7.215 seconds (3 decimal points)

Congratulations!! You have just completed your second lesson in Projectile Motion. You are now an expert on finding the time of flight of a projectile. Its time for you to show us how much you have learnt from this lesson. Brace yourself for these 5 questions. And if can do them you can proceed to the next lesson - Calculating the maximum height.

### Questions

1) An object is fired from the ground. When an object is at half the total time of flight the vertical velocity is:

a) Zero.
b) 9.8m/s.
c) At a maximum.
d) Velocity is negative.

2) What is the time of flight of an object which is dropped from an altitude of 20m?

a) 2.020s.
b) 4.040s.
c) 20s.
d) 1.010s

3) An object is fired with a velocity of 22m/s at 33 degrees to the horizontal. Find the time of flight.

4) A pot-plant is thrown vertically upwards with a velocity 100m/s. Calculate the time taken for the flight.

5) Another projectile is fired with an initial velocity of 25m/s at an angle of 40 degrees above the horizontal. What is the time of flight for this projectile?