i think you have to find it by quadractic way or b- {b2-4ac] divided by 2 times a. i get what you mean but the answer is not right. h(t)=-4.9t2 +16.9t+0.5
To find the solution to the equation h(t) = -4.9t^2 + 16.9t + 0.5, you're right that we can use the quadratic formula. The quadratic formula is:
t = (-b ± √(b^2 - 4ac)) / (2a)
Now, let's plug in the values from our equation into the quadratic formula:
a = -4.9
b = 16.9
c = 0.5
Substituting these values into the quadratic formula, we get:
t = (-16.9 ± √(16.9^2 - 4(-4.9)(0.5))) / (2(-4.9))
Simplifying further:
t = (-16.9 ± √(286.41 + 9.8)) / (-9.8)
t = (-16.9 ± √296.21) / (-9.8)
Now, calculating the square root of 296.21:
t = (-16.9 ± √(17.2^2)) / (-9.8)
t = (-16.9 ± 4.147) / (-9.8)
Using both the plus and minus signs to account for both solutions, we have:
t1 = (-16.9 + 4.147) / (-9.8)
t2 = (-16.9 - 4.147) / (-9.8)
Calculating further:
t1 ≈ (-12.753) / (-9.8) ≈ 1.301
t2 ≈ (-21.048) / (-9.8) ≈ 2.15
Therefore, the solutions to the equation h(t) = -4.9t^2 + 16.9t + 0.5 are approximately t = 1.301 and t = 2.15.