Module8: Motion in Two and Three Dimension
Projectile is a body thrown with an initial velocity in the vertical plane and then it moves in two dimensions
under the action of gravity alone without being propelled by any engine or fuel. Its motion is called projectile
motion.The path of a projectile is called its trajectory.
Gravity, being a downward force, causes a projectile to accelerate in the downward direction. The force of
gravity could never alter the horizontal velocity of an object since perpendicular components of motion are
independent of each other. A vertical force does not effect a horizontal motion. The result of a vertical force
acting upon a horizontally moving object is to cause the object to deviate from its otherwise linear path. This
is depicted in the animation below
Examples:
1.
A packet released from an airplane in flight.
2.
A golf ball in flight.
3.
A bullet fired from a rifle.
4.
A jet of water from a hole near the bottom of a water tank.
Projectile motion is a case of twodimensional motion .Any case of two dimensional motion can be resolved
into two cases of one dimensional motion one along the xaxis and the other along the yaxis.The two cases
can be studied separately as two cases of one dimensional motion.The results from two cases can be
combined using vector algebra to see the net result
A body can be projected in two ways :
1. Horizontal projectionWhen the body is given an initial velocity in the horizontal direction only.
2. Angular projectionWhen the body is thrown with an initial velocity at an angle to the horizontal
direction.
We will study the two cases separately. We will neglect the effect of air resistance. We will take xaxis along
the horizontal direction and yaxis along the vertical direction.
Case 1:
Horizontlal Projection
A body is thrown with an initial velocity u along the horizontal
direction.We will study the motion along x and y axis
separately.We will take the starting point to be at the origin.
Case 2:
Angular Projection
We will now consider the case when the object is
projected with an initial velocity u at an angle to the
horizontal direction.
We assume that there is no air resistance .Also since
the body first goes up and then comes down after
reaching the highest point , we will use the Cartesian
1
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convention for signs of different physical quantities.
The acceleration due to gravity 'g' will be negative as
it acts downwards
.
We will separate the motion into horizontal motion (motion along xaxis) and vertical motion (motion along y
axis) .We will study xmotion and ymotion separately.
Given the original conditions with which the projectile is thrown we will proceed to find the components of the
original velocity and then move on to answer the following questions:
•
Path (trajectory) of the Projectile
•
How much time passes till the projectile is at the top of its flight?
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 Spring '11
 dr.sohrabuddin
 Velocity, tan θ, Vfy, Horizontlal Projection

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