Final answer:
To clear the 3m-high crossbar, the football needs to have a minimum initial speed calculated using projectile motion equations. The football hits the ground after a certain time of flight and the peak height can be calculated using formulas. The time spent by the football in the air can be obtained by doubling the time of flight.
Step-by-step explanation:
The minimum speed the football would need, initially, to clear the crossbar can be found using projectile motion equations. First, we need to split the initial velocity into horizontal and vertical components. Since the football is kicked at 45 degrees to the horizontal, the horizontal component of the velocity will be Vx = V * cos(45) and the vertical component will be Vy = V * sin(45), where V is the initial speed.
To clear the 3m-high crossbar, the ball's maximum height should be greater than or equal to 3m. We can use the maximum height formula to find the value of V:
Hmax = (Vy^2) / (2 * g)
Substituting the value of Vy, we get:
Hmax = (V^2 * sin^2(45)) / (2 * g), where g is the acceleration due to gravity.
The football will hit the ground when its vertical displacement becomes -3m (taking downwards as negative). We can use the vertical displacement formula to find the time of flight:
-3 = Vyt - (1/2) * g * t^2
Simplifying the equation, we get a quadratic equation:
(1/2) * g * t^2 - Vyt - 3 = 0
Solving this quadratic equation, we can find the value of t.
The peak height of the ball is the value of Hmax calculated earlier.
The time the football spends in the air can be found by doubling the value of t obtained earlier.