Solve the following projectile motion problem
aballistossedintotheairat40feetpersecondfromahof5feet.howlongwillittaketheballtoreachtheground
Projectile motion equation:
h(t) = -16t2 + vt + h where:
h = height, v = velocity, and t = time
Plug in our numbers
h(t) = -16t2 + (40)t + 5
When does the object hit the ground:
Set h(t) = 0
-16t2 + 40t + 5 = 0
Evaluate the quadratic
Only take positive values
since height cannot be negative
Quadratic Formula
Calculate -b
-b = -(40)
-b = -40
Calculate the discriminant Δ
Δ = b2 - 4ac:
Δ = 402 - 4 x -16 x 5
Δ = 1600 - -320
Δ = 1920 <--- Discriminant
Since Δ > 0, we expect two real roots.
Take the square root of Δ
√Δ = √(1920)
√Δ = 8√30
-b + Δ:
Numerator 1 = -b + √Δ
Numerator 1 = -40 + 8√30
-b - Δ:
Numerator 2 = -b - √Δ
Numerator 2 = -40 - 8√30
Calculate 2a
Denominator = 2 * a
Denominator = 2 * -16
Denominator = -32
Find Solutions
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
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 Set
(Solution 1, Solution 2) = ((-5 . 1√30)/-4, (-5 - 1√30)/-4)
(Solution 1, Solution 2) = ((-5 . 1√30)/-4, (-5 - 1√30)/-4)
You have 2 free calculationss remaining
What is the Answer?
(Solution 1, Solution 2) = ((-5 . 1√30)/-4, (-5 - 1√30)/-4)
How does the Projectile Motion Calculator work?
Free Projectile Motion Calculator - Solves for time using a height and velocity of an object thrown up in the air
This calculator has 1 input.
What 1 formula is used for the Projectile Motion Calculator?
h(t) = -16t
2 + vt + h where:
h = height, v = velocity, and t = time
For more math formulas, check out our
Formula Dossier
What 4 concepts are covered in the Projectile Motion Calculator?
- height
- the distance from the bottom to the top of something standing upright
- projectile motion
- a form of motion experienced by an object or particle that is projected in a gravitational field
- quadratic equation
- Equation with a polynomial with a maximum term degree as the second degree
- velocity
- speed of an object in a given direction
Example calculations for the Projectile Motion Calculator
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