Can somebody show I how get to 215ft/s for my answer from the following equation 500ft= √3 /2vt - 16*t² with.t= 1600ft/v
in ancient foot units
g = -32 ft/s^2
v = Vi - g t = Vi - 32 t
h = Hi + Vi t +(1/2) a t^2 + Hi + Vi t -16 t^2
evidently here
h = 500
Hinitial = 0
Vi = sqrt (3 / 2) v = initial speed up
t = 1600 / v
500 = 1.225 v (1600/v) - 16 (1600^2)/v^2
500 = 1960 - 4.10*10^7/v^2
4.1*10^7 = 1460 v^2
v^2 = 28055
v = 167 ah well, check my arithmetic
Thank
To find the value of v that makes the equation 500ft = (√3/2)vt - 16t² true, you need to substitute the given value of t into the equation and solve for v.
Given: t = 1600ft/v
Substituting t into the equation:
500ft = (√3/2)v(1600ft/v) - 16(1600ft/v)²
Simplifying this equation step by step:
First, solve the term (√3/2)v(1600ft/v):
(√3/2) * v * (1600ft/v) = (√3/2) * v * (1600/v)
= (√3/2) * (1600)
= 800√3
Now, solve the term -16(1600ft/v)²:
-16 * (1600ft/v)² = -16 * (1600/v)²
= -16 * (1600²/v²)
= -16 * (2560000/v²)
= -40960000/v²
Substituting these values back into the main equation:
500ft = 800√3 - 40960000/v²
To isolate v², subtract 800√3 from both sides:
500ft - 800√3 = -40960000/v²
Next, multiply both sides by v²:
v² * (500ft - 800√3) = -40960000
Finally, divide both sides by (500ft - 800√3) to solve for v²:
v² = -40960000 / (500ft - 800√3)
Now, take the square root of both sides to find v:
v = √(-40960000 / (500ft - 800√3))
Simplifying further:
v ≈ √(-36864 / (5 - 8√3))
At this point, it's not possible to determine a real value for v since the result involves the square root of a negative number.
Therefore, the given equation does not have a valid solution for v.