Emmy kicks a soccer ball up at an angle of 45° over a level field. She watches the ball's trajectory and notices that it lands, two seconds after being kicked, about 20 m away to the north. Assume that air resistance is negligible, and plot the horizontal and vertical components of the ball's velocity as a function of time. Consider only the time that the ball is in the air, after being kicked but before landing. Take "north" and "up" as the positive x ‑ and y ‑directions, respectively, and use g≈10g≈10 m/s2 for the downward acceleration due to gravity

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).

they are non-matter

explanation:

they are non-matter. basically, any type of energy or any abstract concept is an example of something that does not matter. other examples include dreams, magnetism, radio, and hate

the bal will not change its velocity.