A player kicks the football from the ground with a velocity of of 30m/s at 45 degree angle. The time take to reach maximum height was 0.7 s. Find the maximum height and describe your work.

To find the maximum height, we need to break down the motion into two components: horizontal and vertical.

Let's first find the initial vertical velocity (the vertical component of the initial velocity). We know that the initial velocity is 30 m/s, and it was launched at an angle of 45 degrees.

The initial vertical velocity can be found using the formula:

Vertical component of velocity (Vy) = initial velocity (V) * sin(angle)

Substituting the given values:
Vy = 30 m/s * sin(45°)

Sin(45°) is equal to (√2)/2.

Vy = 30 m/s * (√2)/2
Vy = 30√2/2
Vy = 15√2

Now, to find the maximum height reached by the football, we need to calculate the time it takes to reach the maximum height.

Given that the time taken to reach the maximum height is 0.7 seconds, we know that it takes the same amount of time to reach the maximum height and come back down.

In this case, the time of flight is equal to twice the time taken to reach the maximum height:

Time of flight = 2 * Time to reach maximum height

Time of flight = 2 * 0.7 s
Time of flight = 1.4 s

Using this time of flight, we can determine the total vertical displacement (max height) of the football using the formula:

Vertical displacement (or maximum height) = Vy * Time of flight - (0.5 * g * (Time of flight)^2)

Since we only know the initial velocity (V) and not the vertical component (Vy), we can use trigonometry to determine this. We can use the equation:

V = sqrt(Vx^2 + Vy^2)

Since the motion is purely vertical at maximum height, the horizontal component (Vx) will be zero.

Therefore:

V = sqrt(0 + Vy^2)
30 m/s = sqrt(0 + Vy^2)

Simplifying gives us:
900 = Vy^2

Taking the square root of both sides:
Vy = sqrt(900)
Vy = 30 m/s

Now, let's calculate the maximum height:

Max height = Vy * Time of flight - (0.5 * g * (Time of flight)^2)

Max height = 30 m/s * 1.4 s - (0.5 * 9.8 m/s^2 * (1.4 s)^2)
Max height = 42 m - 0.5 * 9.8 m/s^2 * 1.96 s^2
Max height = 42 m - 0.5 * 9.8 m/s^2 * 3.8416 s^2
Max height = 42 m - 0.5 * 9.8 m/s^2 * 3.8416 s^2
Max height = 42 m - 18.9568 m
Max height ≈ 23.0432 m

Therefore, the maximum height reached by the football is approximately 23.0432 meters.

vf=Vivertical-gt

but vf in the vertical is zero at the top, so
0=Vi*sin45-9.8t
solve ford Vi

Height= vivertical*t-1/2 g t^2
= Vi*sin45*t-1/2 g t^2