Final answer:
The gumball took approximately 0.569 seconds to hit the ground. To find the time it took for the gumball to hit the ground, we can use the equation of motion and solve the resulting quadratic equation.
Step-by-step explanation:
To solve this problem, we can use the equation of motion:
d = vt + (1/2)at^2
In this equation, d represents the distance, v represents the initial velocity, t represents the time, and a represents the acceleration.
Since the gumball is rolling off the ledge, we can assume that it is in free fall and the only acceleration acting on it is due to gravity, which is approximately -9.8 m/s^2.
We need to find the time it took for the gumball to hit the ground, so we can set d = 2.3 m, v = 5.21 m/s, and a = -9.8 m/s^2 in the equation.
2.3 = (5.21)t + (1/2)(-9.8)t^2
Now we can solve this quadratic equation to find the value of t.
t^2 - (10.42)t + 2.3 = 0
Using the quadratic formula, we get t = 0.569 s or t = 9.251 s.
Since time cannot be negative, the gumball took approximately 0.569 seconds to hit the ground.