Let be the initial velocity of the soccer ball at an angle of inclination of
with the positive x-axis.
Given that:
The horizontal distance covered by the projectile=20 m
Time of flight, seconds
Acceleration due to gravity, downward.
As "north" and "up" as the positive x ‑ and y ‑directions, respectively.
So,
As the acceleration due to gravity is in the vertical direction, so the horizontal component of the initial velocity remains unchanged.
The x-component of the initial velocity, .
The horizontal distance covered by the projectile
m/s
So, the horizontal component of the velocity is 10 m/s which is constant and the graph has been shown in the figure (i).
Now, [as
]
m/s.
The vertical component of the initial velocity,
m/s
Let v be the vertical component of the velocity at any time instant t.
From the equation of motion,
where u: initial velocity, v: final velocity, a: constant acceleration, and t: time taken to change the velocity from u to v.
In this case, we have .
So at any time instant, t.
The vertical component of the velocity, v, is the function of time and related as .
This is a linear equation.
At 2 second, the vertical component of the velocity
v=10-10x2=-10 m/s.
The graph has been shown in figure (ii).
