To find the time when the golf ball hits the ground, we need to determine when the height (h) becomes zero. The height of the golf ball is represented by the equation:
h(t) = -16t^2 + 20t
To find the time (t) when the golf ball hits the ground (h = 0), set the equation equal to zero and solve for t:
-16t^2 + 20t = 0
Now, let's factor out common terms:
t(-16t + 20) = 0
Now, we have two factors that could be equal to zero:
1. t = 0 (This represents the initial time when the golf ball is hit into the air.)
2. -16t + 20 = 0
Now, solve for t:
-16t + 20 = 0
-16t = -20
t = -20 / -16
t = 1.25
Since time cannot be negative in this context, we discard the t = 0 solution.
Therefore, the golf ball hits the ground after approximately 1.25 seconds.