This is the same equation as before just with different numbers.

y=yo + (vo sin Q) t - 1/2gt^2

This time the numbers are:

0 = 1.005 + (3.021 sin 30)t - 1/2(9.8)t^2

4.9t^2 - 1.5105 - 1.005 = 0
This is the part where I am stuck. Did I do this correctly? sin 30 = 0.50 X 3.021 = 1.5105 and then I would subtract this from 1.005

so then it would be 1.5105 - 1.005 = 0.5055 / 4.9 and square root it.

You are making a similar mistake to yesterday's error.

Yesterday you just magically tagged a t at the end of the first term, now you are dropping the t from the second term

your equation of
0 = 1.005 + (3.021 sin 30)t - 1/2(9.8)t^2
looks ok, assuming your replacement values were correct
then
0 = 1.005 + 1.5105t - 4.9t^2 , since sin 30° = 1/2

4.9t^2 - 1.5105t - 1.005 = 0 , look at yours

you will have to use the quadratic formula

t = (1.5105 ± √(1.5105^2 - 4(4.9)(-1.005) )/9.8
= .... you do the button-pushing

I think you dropped a t:

4.9t^2 - 1.5105t - 1.005 = 0

the coefficients are correct, so now you just have to solve the quadratic equation.

t = 0.154 ± √0.229

To solve the equation 4.9t^2 - 1.5105 - 1.005 = 0, you made some correct steps, but there are a few mistakes in your calculations. Let's break it down step by step:

1. Start with the given equation: 4.9t^2 - 1.5105 - 1.005 = 0

2. Combine like terms: 4.9t^2 - 2.5155 = 0

3. To solve this quadratic equation, we can use the quadratic formula: t = (-b ± √(b^2 - 4ac)) / (2a)

4. Identifying the coefficients in your equation, a = 4.9, b = 0, and c = -2.5155. Plug these values into the quadratic formula:

t = (-(0) ± √((0)^2 - 4(4.9)(-2.5155))) / (2(4.9))

5. Simplify the expression under the square root: √((0)^2 - 4(4.9)(-2.5155)) = √(0 + 49.01(2.5155))

6. Evaluate the expression under the square root: √(123.251199) ≈ 11.09

7. Continue solving for t: t = (0 ± 11.09) / (9.8)

8. Calculate the two possible solutions:

a. t = (0 + 11.09) / (9.8) ≈ 1.13
b. t = (0 - 11.09) / (9.8) ≈ -1.13

So, the two possible solutions for t are approximately 1.13 and -1.13 seconds.

Remember to check the context of the problem to determine if these solutions are valid or if one of them should be disregarded.