The height, h, in feet of a golf ball above the ground after being hit into the air is given by the equation, h = -16t 2 + 64t, where t is the number of seconds elapsed since the ball was hit. How many seconds does it take for the golf ball to hit the ground?
3 seconds?
it hits the ground when the height is zero, right?
-16t 2 + 64t = 0
-16t(t-4) = 0
so, what do you think?
So then t=4?
To find the number of seconds it takes for the golf ball to hit the ground, we need to find the value of t when the height, h, is equal to zero (since the ball is on the ground at that point).
Given the equation for the height of the golf ball is h = -16t^2 + 64t, we set h to zero and solve for t:
0 = -16t^2 + 64t
Since this is a quadratic equation, we can rearrange it to be:
16t^2 - 64t = 0
Now, we can factor out common terms:
16t(t - 4) = 0
To solve this equation, we set each factor equal to zero:
16t = 0 or t - 4 = 0
From the first equation, we see that t = 0 is a possible solution. However, we're interested in the time it takes for the ball to hit the ground, so we'll focus on the second equation:
t - 4 = 0
Solving for t, we find:
t = 4
Therefore, it takes 4 seconds for the golf ball to hit the ground.