A football is kicked at ground level with a speed of 17.9m/s at an angle of 36.0∘ to the horizontal. How much later does it hit the ground?

just a vertical problem

Vi = 17.9 sin 36.0

h = 0 + Vi t - 4.9 t^2
0 = 0 + t (Vi - 4.9 t)
so it is at ground level at t = 0 of course
and
at t = Vi/4.9

Now divide your problems up into vertical problems and horizontal problems

if horizontal speed is u at start it is u to the finish
so
x = u t

if initial vertical speed is Vi
then
v = Vi - 9.81 t (remember v=0 at top)
h = Hi + Vi t - 4.9 t^2

in general if speed is s at A degrees above horizontal

u = s cos A

Vi = s sin A

Now you should be able to do them.

To determine how much later the football hits the ground, we need to break down the initial velocity of the football into its horizontal and vertical components.

The horizontal component of the velocity (Vx) remains constant throughout the motion and is given by:

Vx = V * cosθ

where V is the initial speed of the football (17.9 m/s) and θ is the angle of the kick (36.0 degrees).

Substituting the given values into the equation:

Vx = 17.9 m/s * cos(36.0 degrees)

Now, let's calculate Vx:

Vx = 17.9 m/s * 0.809 (cosine of 36.0 degrees)

Vx ≈ 14.505 m/s

The vertical component of the velocity (Vy) changes due to the effect of gravity. It can be calculated using the equation:

Vy = V * sinθ

where V is the initial speed of the football (17.9 m/s) and θ is the angle of the kick (36.0 degrees).

Substituting the given values into the equation:

Vy = 17.9 m/s * sin(36.0 degrees)

Now, let's calculate Vy:

Vy = 17.9 m/s * 0.588 (sine of 36.0 degrees)

Vy ≈ 10.529 m/s

Next, we can determine the time it takes for the football to hit the ground using the vertical component of the velocity. The time of flight (t) can be calculated using the following equation:

t = (2 * Vy) / g

where g is the acceleration due to gravity (approximately 9.8 m/s^2).

Substituting the values into the equation:

t = (2 * 10.529 m/s) / 9.8 m/s^2

t ≈ 2.148 seconds

Therefore, the football will hit the ground approximately 2.148 seconds after it is kicked.