To determine how long it takes for the ball to hit the ground, we can use kinematic equations and consider the vertical motion of the ball.
Given: Initial vertical velocity (u) = 4 m/s (upward) Vertical displacement (s) = -152.4 m (negative because it's downward motion) Acceleration due to gravity (a) = -9.8 m/s^2 (negative because it's acting in the opposite direction of the initial velocity)
Using the kinematic equation: s = ut + (1/2)at^2, where s is displacement, u is initial velocity, a is acceleration, and t is time, we can rearrange the equation to solve for time:
-152.4 = 4t + (1/2)(-9.8)t^2
This equation is in the form of a quadratic equation: at^2 + bt + c = 0, where: a = (1/2)(-9.8) = -4.9 b = 4 c = -152.4
We can use the quadratic formula to solve for t:
t = (-b ± sqrt(b^2 - 4ac)) / (2a)
Substituting the values, we get:
t = (-(4) ± sqrt((4)^2 - 4(-4.9)(-152.4))) / (2(-4.9))
Simplifying further:
t = (-4 ± sqrt(16 - 2983.2)) / (-9.8) t = (-4 ± sqrt(-2967.2)) / (-9.8)
Since the square root of a negative number is not a real number, we can conclude that the ball will not hit the ground and will never reach a height of -152.4 m. There must be some error or unrealistic assumption in the initial conditions or calculations. Please double-check the given information or provide additional details for further analysis.