3. A ball is thrown into the air with an initial upward velocity of 46ft/s. Its height (h) in feet after t seconds is given by the function h = -16t^2 + 46t + 6. After how many seconds will the ball hit the ground?
A. 3
B. 4
C. 5
D. 6
I think D, if i'm wrong can one of you guy help me thanks
To find the time when the ball hits the ground, we need to determine when the height (h) is equal to zero.
Given the function h = -16t^2 + 46t + 6, we set h = 0 and solve for t:
0 = -16t^2 + 46t + 6
To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac)) / (2a)
Where a = -16, b = 46, and c = 6.
Substituting the values into the formula:
t = (-46 ± sqrt(46^2 - 4(-16)(6))) / (2(-16))
Simplifying:
t = (-46 ± sqrt(2116 + 384)) / (-32)
t = (-46 ± sqrt(2500)) / (-32)
t = (-46 ± 50) / (-32)
There are two possible solutions, one with the positive sign and one with the negative sign:
t1 = (-46 + 50) / (-32) = 4 / (-32) = -1/8
t2 = (-46 - 50) / (-32) = -96 / (-32) = 3
Since time cannot be negative, the ball hits the ground after 3 seconds. Thus, the answer is A. 3
To find out when the ball hits the ground, we need to determine the value of t when the height (h) is equal to zero.
Given the equation for the height of the ball: h = -16t^2 + 46t + 6
To find out when the ball hits the ground, we set h equal to zero and solve for t:
0 = -16t^2 + 46t + 6
This equation is a quadratic equation, and we can solve it by factoring or by using the quadratic formula.
In this case, it's easier to use the quadratic formula:
t = (-b ± √(b^2 - 4ac))/(2a)
Where a, b, and c are the coefficients of the quadratic equation:
a = -16
b = 46
c = 6
Plugging these values into the formula, we have:
t = (-46 ± √(46^2 - 4(-16)(6))) / (2(-16))
t = (-46 ± √(2116 + 384)) / (-32)
t = (-46 ± √2500) / (-32)
We can simplify further:
t = (-46 ± 50) / (-32)
Now we have two possible values for t:
t1 = (-46 + 50) / (-32) = 4/(-32) = -1/8
t2 = (-46 - 50) / (-32) = -96/(-32) = 3
Since time cannot be negative in this context, we discard the negative value (-1/8) and conclude that the ball hits the ground after 3 seconds.
Therefore, the correct answer is A. 3.
well, did you check it?
-16*36 + 46*6 + 6 = -294
So, stop guessing and do the math!
h = -2(8t^2-23t-3)
= -2(8t+1)(t-3)
So now what do you think?