y=1.5 + 76.95t-(1/2)(9.8)t2 = 303.6
I am not sure how to arrive at this answer. I am confused because there is a t and a t^2. Thank you for your help!
Use the quadratic formula.
You be able to do work of this nature you MUST have learned how to solve a quadratic equation.
Yes but I always set it up incorrectly.
so [76.95 +/- sqrt (76.95^2 - 4(4.9)(-1.5)] / 9.8
Did I set this up correctly?
-4.9t^2 + 76.95t - 302.1 = 0
4.9t^2 - 76.95t + 302.1 =0
a=4.9
b=76.95
c=302.1
t = (76.95 ± √(76.95^2 - 4(4.9)(302.1))/9.8
see if you can get t = 18.856 or -3.252
what happened to your 303.6 in the opening equation?
I was using this equation as an example to try to help myself understand something but I think I may have set it up incorrectly. What I am trying to do is find the y max of a projectile using the equation y = yo + (vo sin Q ) t -1/2gt^2.
I keep plugging in my values for the angles and vO but I cant seem to get y.
Please disregard. Thank you.
The equation you provided is a quadratic equation in terms of the variable t. This type of equation can be solved using the quadratic formula or by factoring. Let's go through the steps to solve it using the quadratic formula:
1. Rearrange the equation into the standard quadratic form:
(1/2)(-9.8)t^2 + 76.95t + 1.5 - 303.6 = 0
2. Multiply both sides of the equation by 2 to get rid of the fraction:
-4.9t^2 + 153.9t + 3 - 607.2 = 0
3. Combine like terms:
-4.9t^2 + 153.9t - 604.2 = 0
4. Now we can use the quadratic formula to solve for t:
t = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = -4.9, b = 153.9, and c = -604.2
5. Plug these values into the quadratic formula and solve for t:
t = (-153.9 ± √(153.9^2 - 4*(-4.9)*(-604.2))) / (2*(-4.9))
Simplify the expression under the square root:
t = (-153.9 ± √(23793.21 + 11846.88)) / (-9.8)
Simplify further:
t = (-153.9 ± √35640.09) / (-9.8)
6. Take the square root of 35640.09:
t = (-153.9 ± 188.81) / (-9.8)
7. Solve for t using both the positive and negative values:
t1 = (-153.9 + 188.81) / (-9.8) = 3.75
t2 = (-153.9 - 188.81) / (-9.8) = -40.66
Therefore, the values of t that satisfy the equation are t = 3.75 and t = -40.66.
To verify these solutions, you can substitute them back into the original equation and check if they make it true.