Projectile Motion - Components of velocity

To understand projectile motion, the first concept you should grasp is the idea that a projectile's total velocity can be split into two components, horizontal and vertical velocity.

Figure 1.
	Let u = initial object velocity x = angle of projection, u_h = horizontal velocity u_v = initial vertical velocity

If an object is fired at an angle of ‘x’ with total velocity ‘u’, calling on our basic knowledge of trigonometry, we can see from the above diagram that,

u_h / u = sinx thus, u_h = u sinx u_v / u = cosx thus, u_v = ucosx

u_h = ucosx
u_v = usinx

u_h = horizontal velocity (m/s)
u_v = initial vertical velocity (m/s)
u = initial velocity of object (m/s)   x = angle of projection (degrees)

Q: A projectile was launched with the total velocity of 100m/s at an angle of 30 degrees.

(a) Find its vertical velocity.
(b) Find its horizontal velocity.

A:
(a)
Total velocity, 'u', = 100m/s.
As seen from the formula in the table, U_v = usinx. Therefore:
U_v= 100 x sin 30 = 100 x 0.5 = 50 m/s.

(b)

U_h = ucosx. Therefore:
U_h= 100 x cos 30 = 86.603 m/s (3 decimal places)

Congratulations!! You have just completed your first lesson in Projectile Motion. You are now an expert on the different components of a projectile's velocity. Its time for you to show us how much you have learnt from this lesson. Have a go at these 5 questions. And if you're smart enough to complete them you'll be taken to the next lesson, finding the total time of a projectile's flight.

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As you can see it is really simple to find the vertical and horizontal components of a projectile's velocity, and now you're ready for the next lesson, finding the total time of a projectile's flight.