A body projected horizontally from a certain height with an
initial horizontal velocity can be called as a horizontal projectile. Its
initial velocity along the vertical direction is zero and it possess only
horizontal velocity at the beginning. As the time progresses, due to the impact
of the gravity, it acquires the vertical component of velocity also. It can be
shown that path taken by this body is parabola using the equations of motion of
kinematics. We can write the equations for the displacement along x-axis and
y-axis and further substituting the value of the time from the x-axis equation in
the y-axis equation, it can be proved that its path is parabola.

At any instant of the path, velocity of the projectile is
tangential to its path. It has both horizontal and vertical components and the
angle made by the velocity vector with the horizontal can be calculated as
shown below. We can also calculate the effective velocity of the projectile at
that instant.

**Application**

Let us consider a body projected horizontally from the top of
a tower. The line joining the point of projection and the striking point of
ground makes an angle of 45° with the horizontal. What is the displacement of the body?

**Solution**

As the angle made at the horizontally is 45 degree, according
to trigonometry, its horizontal and vertical distances are equal. Being the
displacement is a vector quantity with can calculate its resultant value using
the parallelogram law of the vectors as shown below.

**Application**

Let us consider a ball is thrown horizontally from a staircase
as shown with a initial velocity. We shall calculate how many steps it travels
before it strikes the ground?

**Solution**

The ball is having only horizontal component of velocity and
has no initial vertical component of velocity.

We can use equations of motion to find the displacement along
x-axis and y-axis. There is no acceleration due to gravity impact on the x-axis
and there is gravity acting along the y-axis. The total horizontal distance
travelled by the body is equal to the multiplication of the number of the steps
and the breadth of each step. Similarly the total vertical distance travelled
by the body is equal to the multiplication of number of steps with the height
of each step.

By substituting this values in the above equation is can solve
the problem as shown below.

**Application:**

Two bodies are thrown horizontally with a two different
initial velocities in mutually opposite directions from the same height. What
is the time after which velocity is of the two bodies are perpendicular to each
other ?

**Solution:**

Velocity is a physical quantity that is having both magnitude
and direction and it has to be treated like a vector quantity. When two vectors
are perpendicular to each other their scalar product becomes zero. Taking this
into consideration and by writing the equations of velocity is for the two
bodies after a specific time and equating their product to 0 with can solve the
problem as shown below.

**Problem**

An object is thrown horizontally from a point it hits the ground
at some another point. The line of sight from these two points makes an angle
60° with the horizontal. If acceleration due to gravity is 10 m/s Squire and
time of flight is known what is the velocity of projection?

**Solution**

by writing the equations were displacement along x-axis and
y-axis and by using a trigonometrical definition we can solve the problem as
shown below.

**Problem**

Two paper screens are separated by a distance of hundred
meter. A bullet fired through them. The hole made in the second screen is 10 cm
below the hole made in the first screen. What is its initial velocity before it
strikes the first screen?

**Solution**

Initially the bullet is having only horizontal velocity and
its vertical component of velocity equal to 0. There is no impact of
acceleration due to gravity along the x-axis and it is acting along the y-axis.
Taking this things into consideration we can equate the distance between the
two poles along the vertical direction is equal to the vertical distance
travelled by the body during the journey time. We can also calculate the time
taken by the body for this to happen using the equation of the displacement
along the x-axis. By solving these equations together we can calculate the
initial velocity of the projection as shown below.

**Related Posts**

**Distance and displacement**

__comparison__
## No comments:

## Post a Comment