An object is dropped from a hot-air balloon 1296 feet above the
ground. The height of the object is given by
h=-16(t-9)(t+9)
where the height h is measured in feet, and the time t is measured in seconds.
After how many seconds will the object hit the ground?
978
To find the time at which the object hits the ground, we need to solve for t when h equals 0 (since the height will be 0 when it hits the ground).
The given equation for the height of the object is:
h = -16(t-9)(t+9)
Setting h = 0, we have:
0 = -16(t-9)(t+9)
Now, since the product of two numbers is zero only if at least one of the numbers is zero, we can set each factor equal to zero and solve for t:
t - 9 = 0 or t + 9 = 0
For t - 9 = 0, we add 9 to both sides:
t = 9
For t + 9 = 0, we subtract 9 from both sides:
t = -9
So, the object hits the ground at t = 9 seconds or t = -9 seconds.
However, since time is measured in seconds and it doesn't make sense to have a negative time, we can disregard t = -9 seconds.
Therefore, the object hits the ground after 9 seconds.