If an object is dropped from a height of 144 ft, the function h(t) = –16t² + 144 gives the height of the object after t seconds. When will the object hit the ground?
• 1.5 s
• 3 s
• 6 s
• 9 s
it will hit the ground when the height h(t) = 0
-16t^2 + 144 = 0
16t^2 = 144
t^2 = 144/16 = 9
so t =√9 = 3
after 3 seconds
That helps alot - Thanks.
To find when the object hits the ground, we need to determine the value of t when the height h(t) becomes 0.
Given the function h(t) = -16t² + 144, we can set it equal to 0:
-16t² + 144 = 0
To solve this quadratic equation, we can factor out common terms:
-16(t² - 9) = 0
Since the equation is equal to 0, we can set each factor equal to 0:
t² - 9 = 0
Now, we can solve for t by factoring or by using the quadratic formula. In this case, we can factor the equation as a difference of squares:
(t - 3)(t + 3) = 0
To find the values of t, we set each factor equal to 0:
t - 3 = 0 or t + 3 = 0
Solving these equations, we get:
t = 3 or t = -3
However, time cannot be negative in this case, so we discard t = -3.
Therefore, the object hits the ground at t = 3 seconds.
So the correct answer is:
• 3 s
To find the time when the object hits the ground, we need to find the value of t when h(t) is equal to 0. In this case, h(t) represents the height of the object at time t.
Given the function h(t) = -16t^2 + 144, we can set h(t) equal to 0 and solve for t:
-16t^2 + 144 = 0
Now, we can solve this quadratic equation for t. Rearranging the equation:
16t^2 = 144
Dividing both sides of the equation by 16:
t^2 = 9
Taking the square root of both sides:
t = ±√9
Since we are dealing with time, we can ignore the negative value. Therefore:
t = √9
t = 3
So, the object will hit the ground after 3 seconds.
Therefore, the correct option is:
• 3 s