An object is dropped from a height of 80 ft The function h (t)-16t 2 + 80 gives the height of the object after t seconds approximately when will the object hit the ground Will it hit after 1 second Will it hit after 5 seconds Will it hit after 16 seconds or will it hit after 2 seconds
To determine when the object will hit the ground, we need to find the value of t when h(t) equals zero.
Setting h(t) = 0, we get:
0 = -16t^2 + 80
To solve this quadratic equation, we can factor out a common factor of 16:
0 = 16(-t^2 + 5)
Now, we set each factor equal to zero and solve for t:
- t^2 + 5 = 0
Adding t^2 to both sides of the equation:
t^2 = 5
Taking the square root of both sides:
t = ±√5
Since time cannot be negative in this context, we discard the negative solution.
So, the object will hit the ground approximately after √5 seconds.
Using a calculator, we can approximate √5 ≈ 2.236.
Therefore, the object will hit the ground after approximately 2.236 seconds.
So, it will hit the ground after 2 seconds.