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≈10 m/s2 for the downward acceleration due to gravity.

v_y = 10 - 10t

v_x = 10 m/s

Explanation:

This is a projectile launch where the x axis and y axis will be treated independently.

Now, towards the north on the x-axis, there will be no acceleration and so the speed is constant

So, vₓ = v₀ₓ

Whereas, on the vertical y - axis, the acceleration due to gravity with be negative since it's in a downward direction.

Thus, the equation is;

v_y  =  v_oy - gt

Now, the initial velocity component will be;

cos 45 = v₀ₓ/v₀

And sin 45 = v_₀y/v₀

Thus, we have;

v₀ₓ = v₀(cos 45)

Also, v_oy = v₀(sin 45)

Now, the initial velocity would be gotten from the equation of range which is;

R = (v₀² × sin 2θ)/g

Making v₀ the subject, we have;

v₀ = √(Rg/sin 2θ)

We are given;

R = 20 m

g = 10 m/s²

θ = 45°

Thus;

v₀ = √[20 × 10/(sin (2 × 45))]

v₀ = √200

v₀ = 14.14 m/s

Thus;

v₀ₓ = 14.14(cos 45) = 10 m/s

v_oy = 14.14(sin 45) = 10 m/s

Earlier we saw that;

v_y  =  v_oy - gt

Thus;

v_y = 10 - 10t

Also,we saw that;

vₓ = v₀ₓ

Thus;

v_x = 10 m/s

For the graph, we will use times of  t = 0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2

Thus, for each of those values of t, we will have the following values of v_oy

t (s)       v_oy (m / s)

0           10

0.2         8

0.4          6

0.6         4

0.8          2

1.0         0

1.2          -2

Graph is attached

car a and b are moving in opposite directions

plz mark.me the brainliest i rlly need this kind of yours in exchange

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation: