l
Solve the following projectile motion problem
aballistossedintotheairat40feetpersecondfromahof5feet.howlongwillittaketheballtoreachtheground
h(t) = -16t2 + vt + h where:
h = height, v = velocity, and t = time
h(t) = -16t2 + (40)t + 5
Set h(t) = 0
-16t2 + 40t + 5 = 0
Only take positive values
since height cannot be negative
= | -b ± √b2 - 4ac |
2a |
-b = -(40)
-b = -40
Δ = b2 - 4ac:
Δ = 402 - 4 x -16 x 5
Δ = 1600 - -320
Δ = 1920 <--- Discriminant
Since Δ > 0, we expect two real roots.
√Δ = √(1920)
√Δ = 8√30
Numerator 1 = -b + √Δ
Numerator 1 = -40 + 8√30
Numerator 2 = -b - √Δ
Numerator 2 = -40 - 8√30
Denominator = 2 * a
Denominator = 2 * -16
Denominator = -32
Solution 1 = | Numerator 1 |
Denominator |
Solution 1 = (-40 + 8√30)/-32
Analyzing the 3 terms in our 1st answer
We see that -40, -32, and 8 are all divisible by 8
Dividing them all by 8, we get: -5, -4, and 1
Solution 1 = (-5 . 1√30)/-4
Solution 2 = | Numerator 2 |
Denominator |
Solution 2 = (-40 - 8√30)/-32
Analyzing the 3 terms in our 1st answer
We see that -40, -32, and 8 are all divisible by 8
Dividing them all by 8, we get: -5, -4, and 1
Solution 2 = (-5 - 1√30)/-4
(Solution 1, Solution 2) = ((-5 . 1√30)/-4, (-5 - 1√30)/-4)