Projectile motion

Imagine you are throwing a stone towards the sky. Does it move in a straight line? does it reach back to the same point from where you have started throwing? Well, the answer is no becasue the motion here is a forward and upward in nature, resulting in reverse U-shaped motion called projectile motion. Projectile motion is the result of 2 directional simultaneous movement. The 2 movements are the independent rectilinear motions. It is responsible for the horizontal forward and upward motion of the object along the X-axis and after reaching its peak, there is a downward movement forming a parabolic curve. In the projectile motion, the object is called a projectile, and its path is called its trajectory.

 

 

Definition

When an object is thrown upwards at an angle to the horizontal/vertical line, it takes a parabolic path. This is called projectile motion. The only force acting on the object is the gravitational force. So a projectile motion is the combination of 2 components in the horizontal and vertical directions.

Trajectory in a projectile motion

  Trajectory in a projectile motion

 

 

 

Consider an object projected with a velocity u0, with an angle θ to the horizontal. The velocity of the vector can be resolved into the horizontal and vertical components,i,e  respectively.  The gravitational force will act only on the vertical motion of the object. Therefore the vertical movement of the object will be similar to an object thrown upwards. The vertical component of the velocity will decrease along the path until it reaches the highest point and then increases while it returns back. But as there is no external force acting on the horizontal motion the velocity of the horizontal component will remain the same. The pictures below depict the nature of the movement of objects in a parabolic path. The first figure shows the two velocity components of the projectile motion. The second figure shows the path taken by the object and the change of velocity along the path. The length of the arrows gives us an idea of the magnitude of the velocity. The length of the vertical arrow decreases and becomes zero at the highest point and then begins to increase again. But the length of the vertical arrow remains the same throughout the motion. This explains how the velocity changes along the path.

 

 

 

Applying the equations of motion for a projectile

Consider the above situation where an object is projected with an initial velocity u0 with an angle θ to the horizontal. Considering the vertical motion of the object, the maximum height travelled by the object is

 

 

 

The time taken for the complete motion is called the time of flight and is two times the above, due to the symmetry of the motion.  Considering the horizontal motion of the object, the range (R) is calculated as 

                                                            

 

The range is the horizontal distance travelled by the object. The time taken is equal to the time of flight and the acceleration is zero.

 

An Object is projected with an initial velocity of 5 m/s, 30⁰ to the horizontal. Find the maximum height, the time of flight, the range and the vertical velocity after 0.2 s? 

Answer:

 

          

 

Two objects A and B are projected with an angle 30⁰ and 60⁰ to the horizontal respectively. The time of flight is the same for both objects.  What is the ratio between the initial velocities of the two objects?

  1. 2 : √3         b) √3 : 2           c) 1 : √3           d) √3 : 1

Answer: (d) 


 



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