Using the equation
y=yo + (vo sin Q) t - 1/2gt^2 I have to find t. The values for y, yo and vo were given to me.
So I set the equation up like this:
0=1.005 + (3.107 sin 0) t - 1/2(9.8)(t^2
The sin of 0 is 0 times 3.107 is 0.
So 0 = 1.005 t - 4.9 t^2
Now I am stuck. I am not sure how to solve this part. Thank you for your help!
you would get
4.9t^2 - 1.005t = 0
t(4.9t - 1.005) = 0
t = 0 or t = 1.005/4.9 = 201/980 or appr .205
Where do you get the 1.005t? It appears to me that you just stuck a t onto the number 1.005.
The 1.005 was the value given for yo, the angle given was 0 and vo was 3.107. The t I just took from the equation
y=yo + (vo sin Q) t -1/2 gt^2.
I need to find t using this equation but I wasn't sure how to do it.
I never even looked at the equation that closely, just assumed she did the subbing correctly
now it would simply be
4.9t^2 = 1.005
t = ± √(1.005/4.9) = appr .45
I may be dense but I still don't get it. if yo is 1.005, that's the number that goes into the equation for yo. There is no t there. The equation would have to be yo*t for that to be true. right?
Ahh! I haven't forgotten ALL my math. Just most of it
assuming her values were valid and she subbed them in correctly
0=1.005 + (3.107 sin 0) t - 1/2(9.8)(t^2
4.9t^2 - 0 - 1.005 = 0
4.9t^2 = 1.005
t^2 = 1.005/4.9
t = ± √(1.005/4.9) = appr .45
Ok so just to make sure I take the square root of 1.005/4.9= 0.45 which would be both positive and negative but I only take the negative correct? Thank you for your help. This makes sense now because I have to compare this value to the actual which was 0.44 so I am not to far off.
To solve the equation 0 = 1.005 t - 4.9 t^2, you can rearrange it to form a quadratic equation in the form of ax^2 + bx + c = 0, where x represents t.
0 = -4.9 t^2 + 1.005 t
Now, you can use the quadratic formula to solve for t. The quadratic formula states that for an equation in the form of ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = -4.9, b = 1.005, and c = 0.
Plugging these values into the quadratic formula, you get:
t = (-1.005 ± √(1.005^2 - 4(-4.9)(0))) / (2(-4.9))
t = (-1.005 ± √(1.010025 + 0)) / (-9.8)
t = (-1.005 ± √1.010025) / (-9.8)
Now you just need to calculate the two possible solutions for t by separately taking the "+ √" and "- √" parts:
t1 = (-1.005 + √1.010025) / (-9.8)
t2 = (-1.005 - √1.010025) / (-9.8)
Simplifying these expressions, you will find the numerical values for t1 and t2.