Final answer:
The ball took approximately 7.3125 seconds to reach the ground.
Step-by-step explanation:
To find how long the ball took to reach the ground, we can use the equations of motion for vertically thrown objects. In this case, the initial vertical velocity is 117 feet/sec and the acceleration due to gravity is -32 feet/sec^2. Since the ball is thrown upwards and returns to the ground, the final position is the same as the initial position, which is 0 feet. We can use the equation:
0 = 117t - (32/2)t^2
Simplifying the equation, we get
-16t^2 + 117t = 0.
Factoring out t, we have t(-16t + 117) = 0.
So, either t = 0 or -16t + 117 = 0.
Since time cannot be 0, we solve for -16t + 117 = 0 and find t = 7.3125 seconds.
Therefore, the ball took approximately 7.3125 seconds to reach the ground.