**Projectile Motion Formula : Projectile Motion Formula - Definitions, Formula for Projectile Motion**

Now we discuss some example of curved motion or two dimensional motion of constant acceleration such as the motion of constant acceleration such as the motion of a particle projected at certain angle with the horizontal in vertical x-y plane (this type of motion is called projectile motion). Air resistance to the motion of the body is to be assumed absent in this type of motion.

A body projected into the space and is no longer being propelled by fuel is called a projectile.

To analyze the projectile motion we use the following concept "Resolution of two dimensional motion into two one dimension motion" as discussed earlier. Hence it is easier to analyze the motion of projectile as composed of two simultaneous rectilinear motions which are independent of each other:

(a) Along the vertical y-axis with a uniform downward acceleration 'g' and

(b) Along the horizontal x-axis with a uniform velocity forward.

Consider a particle projected with an initial velocity u at an angle Î¸ with the horizontal x-axis as shown in figure shown below. Velocity and accelerations can be resolved into two components:

Velocity along x-axis = ux = u cos Î¸

**Did You KNow**

- Every projectile experiences one single force and that is due to gravity only.
- Horizontal velocity of a projectile remains the same throughout its flight (it may be zero also).
- No projectile ever experiences any acceleration in the horizontal direction.
- Vertical acceleration of every projectile is ‘-g’.
- The path of projectile is parabolic except for those projected along vertical direction. In that case it is a straight line.
- The horizontal and vertical motion of a projectile are independent of each other.

**Question 1:-**

Which of the following is not a projectile:

(a) a bullet fired from a rifle ** (b) a bomb dropped from an aeroplane**

(c) a cricket ball moving in space (d) hydrogen balloon floating in air

**Question 2:-**

A Particle is Projected Horizontally from the Top of a Tower

A particle projected horizontally from the top of a tower clears range equal to the height of a tower. The path described is a part of a:

(a) circle (b) ellipse

(c) hyperbola ** (d) parabola**

**Question 3:-**

A particle is thrown vertically upward. At its highest point, it has:

(a) an upward velocity (b) downward velocity

(c) an upward acceleration ** (d) a downward acceleration**

**Question 4:-**

A particle is thrown vertically upward. Its velocity at half of the height is 10 m/s, then maximum height attained by it:

(a) 8 m (b) 20 m

**(c) 10 m ** (d) 16 cm

**Question 5:-**

A body is projected horizontally from the top of a tower 19.6 meter high. It reaches the ground in:

(a) 1 sec ** (b) 2 sec**

(c) 2.5 sec (d) 5 sec