I am trying to solve a math problem, but Im stuck!

Question

 I know I have to use the quadratic formula, but not sure how to get started.  x=x0+v0t+(1/2)at^2, solve for t

Answer 1

x=x₀+v₀t+(1/2)at², solve for t

 

First, put it in standard form & remember that even though this equation seems like all variables, x₀, v₀, and a are constants represented by letters (like π - pi). x (height) depends on t (time) which are the two variables that will actually vary.

 

In this case, a represents gravitational pull, v₀ represents initial velocity, and x₀ represents initial height. I am going to change that a to  g for clarity when it comes time to plug numbers into quadratic formula.

 

Standard form:

x = (1/2)gt² + v₀t + x₀

 

Now identify a, b, c from y = ax² + bx + c

to plug into quadratic formula x = [ -b ± √(b² - 4ac) ]  / [2a]

a = (1/2)g  = g/2

b = v₀

c = x₀

 

Time to "plug in":

t = [ -v₀ ± √(v₀² - 4(g/2)(x₀) ) ] / [2(g/2)]     (simplify the fractions)

t = [ -v₀ ± √(v₀² - 2gx₀ ) ] / [g]  (switch the g back to an a so the original question is answered)

t = [ -v₀ ± √(v₀² - 2ax₀ ) ] / [a]

 

 

Hope this helps!