I need help this is for homework this problem but i feel like i can't solve because i am missing some information or am i wrong. If so what am i suppost to do...help me
THe height "h" in feet of an object after "t" seconds is given by the function :
h = -16t^2+70t+8
How long will it take the object to hit the ground? Round answer to the nearest thousandsth.
The ground is at h=0. That is the information you need.
0= -16t^2+70t+8
solve for t. Notice it is a quadratic, and has two solutions. In this case, ignore the negative solution (you can think out why).
To solve the equation -16t^2 + 70t + 8 = 0, you can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Where a, b, and c correspond to the coefficients in the equation. In this case, a = -16, b = 70, and c = 8.
Plugging these values into the quadratic formula, we get:
t = (-(70) ± √((70)^2 - 4(-16)(8))) / (2(-16))
Simplifying further:
t = (-70 ± √(4900 + 512)) / (-32)
t = (-70 ± √5412) / (-32)
Now, to find the positive solution, we ignore the negative solution, which is not applicable to this problem. You can see that the object cannot have a negative time.
Calculating:
t ≈ (-70 + √5412) / (-32)
Solving this expression:
t ≈ 4.2827
Rounding to the nearest thousandth:
t ≈ 4.283
Therefore, it will take approximately 4.283 seconds for the object to hit the ground.