Explanation:
We can use the kinematic equations of motion to solve this problem. Let's assume the initial velocity of the snowball is 18 feet per second and its initial height is 25 feet. Also, we know that the acceleration due to gravity is -32.2 feet per second squared (assuming downward direction as negative).
To find out when the snowball hits the ground, we can use the equation:
h = 25 + 18t - 16t^2
where h is the height of the snowball at time t. We want to find the value of t when h = 0 (since the snowball hits the ground at that point). Therefore, we can rewrite the equation as:
16t^2 - 18t - 25 = 0
Solving for t using the quadratic formula, we get:
t = (18 ± √(18^2 + 41625))/(2*16)
t = 2.25 seconds or -0.875 seconds
Since time cannot be negative, the snowball hits the ground after 2.25 seconds.
To find the maximum height the snowball reaches, we can use the fact that the maximum height occurs at the vertex of the parabolic trajectory. The x-coordinate of the vertex is given by:
t = -b/2a
where a and b are the coefficients of the quadratic equation. In this case, a = -16 and b = 18, so:
t = -18/(2*(-16)) = 0.5625 seconds
To find the corresponding height, we can substitute t = 0.5625 seconds into the equation for h:
h = 25 + 18(0.5625) - 16(0.5625)^2
h = 28.2656 feet
Therefore, the maximum height the snowball reaches is 28.2656 feet.