Assuming no air resistance, we can use the kinematic equation for vertical motion:
h = v_it - 0.5g*t^2
where h is the height, v_i is the initial velocity, g is the acceleration due to gravity (32.2 feet per second squared), and t is the time.
To find the maximum height, we need to determine the time it takes for the ball to reach its peak, which occurs when its vertical velocity is zero. The vertical velocity decreases at a rate of g, so the time it takes to reach the peak can be found by:
0 = v_i - g*t_max
t_max = v_i/g
t_max = 45/32.2
t_max ≈ 1.4 seconds
We can now find the maximum height by plugging in this time into the height equation:
h_max = v_it_max - 0.5g*t_max^2
h_max = 451.4 - 0.532.2*(1.4)^2
h_max ≈ 44.4 feet
Therefore, the maximum height the soccer ball will reach is approximately 44.4 feet.
To find the height of the ball at 2 seconds, we can simply plug in t = 2 into the height equation:
h(2) = v_i2 - 0.5g*(2)^2
h(2) = 452 - 0.532.2*(2)^2
h(2) ≈ 40.4 feet
Therefore, the height of the ball at 2 seconds is approximately 40.4 feet.