A football is kicked 65 m. If the ball is in the air for 4.3 s, find its horizontal velocity vx. Enter m/s as unit and use g = 10. m/s2.

What is its initial vertical velocity vy? Enter m/s as unit.
With what initial speed was the football kicked? Enter m/s as unit.

To solve these questions, we can use basic kinematic principles of motion. We can use the equations of motion to find the horizontal velocity, the initial vertical velocity, and the initial speed of the football.

1. Finding the horizontal velocity (vx):
Since the ball is moving horizontally, there is no acceleration acting on it in that direction. Therefore, the horizontal velocity of the ball remains constant during its flight.

The equation to calculate the horizontal distance traveled (x) is given by:
x = vx * t
where x is the horizontal distance traveled, vx is the horizontal velocity, and t is the time of flight.

Given that x = 65 m and t = 4.3 s, we can rearrange the equation to solve for vx:
vx = x / t
= 65 m / 4.3 s
≈ 15.12 m/s

Therefore, the horizontal velocity (vx) of the football is approximately 15.12 m/s.

2. Finding the initial vertical velocity (vy):
The vertical motion of the ball is affected by gravity. The equation to calculate the height (y) reached by the ball is given by:
y = vy * t - (1/2) * g * t^2
where y is the vertical distance, vy is the vertical velocity, t is the time of flight, and g is the acceleration due to gravity (given as 10 m/s^2).

At the maximum height, the vertical velocity becomes zero (vy = 0). Therefore, we have:
0 = vy * t - (1/2) * g * t^2

Simplifying the equation and rearranging, we can solve for vy:
vy = (g * t) / 2
= (10 m/s^2) * (4.3 s) / 2
= 21.5 m/s

Therefore, the initial vertical velocity (vy) of the football is 21.5 m/s.

3. Finding the initial speed of the football:
The initial speed of the football can be calculated using the Pythagorean theorem, as the initial speed is the resultant velocity of the horizontal and vertical components.

The equation to calculate the initial speed (v) is given by:
v = sqrt(vx^2 + vy^2)
where vx is the horizontal velocity and vy is the initial vertical velocity.

Using the values previously calculated:
v = sqrt((15.12 m/s)^2 + (21.5 m/s)^2)
≈ sqrt(228.1344 m^2/s^2 + 462.25 m^2/s^2)
≈ sqrt(690.3844 m^2/s^2)
≈ 26.27 m/s

Therefore, the initial speed of the football is approximately 26.27 m/s.