Answer:
6.5 seconds
Explanation:
This question may be solved in two different ways. We'll use both:
1. Differentiate
The first derivative of an equation allows one to determine the instantaneous slope of that equation for any point, x, along that line. The golf ball will have a trajectory in which the golf ball initially rises and then the force of gravity slows it down to the point that it reverses direction and falls back to Earth. The term -16t^2 in the equation consists of the -16, which is the acceleration due to gravity. It becomes increasingly negative with time. The term 208t is the height achieved at time t. The unit of 224 represents the starting elevation of the golf ball.
When the ball reaches its maximum height, it changes direction from up to down. The slope goes from positive (going up) to negative (falling down). At the exact instant the ball changes directions, the slope of the line is 0, It goes from positive to negative, passing through a point of zero slope.
By setting the first derivative of the equation to zero, we can calculate the value of t:
h(t)=-16t^(2)+208t+224
Take the first derivative:
h(t)=-16t^(2)+208t+224
h'(t) = -32t + 208
0 = -32t + 208
32t = 208
t = 6.5 sec
At 6.5 seconds, the slope is zero. It has reached its maximum height.
1. Graph
We can also graph the function and look for the highest point the golf ball reaches, See the attached graph.
We also get a time of 6.5 seconds. The ball reaches a maximum height of 900 before falling.