## Set up the projectile motion equation:

h(t) = -16t

^{2} + vt + h where:

h = height, v = velocity, and t = time

## Plug in our numbers to the projectile motion equation:

h(t) = -16t

^{2} + (40)t + 5

## Since we want the time when the object hits the ground, we set h(t) = 0:

-16t

^{2} + 40t + 5 = 0

Since this is a quadratic equation, we solve it, ignoring any negative values, since height cannot be negative

`The quadratic formula is denoted below:`

__Step 1 - calculate negative b:__ -b = -(40)

-b = -40

__Step 2 - calculate the discriminant Δ:__Δ = b

^{2} - 4ac:

Δ = 40

^{2} - 4 x -16 x 5

Δ = 1600 - -320

Δ = 1920 <--- Discriminant

Since Δ is greater than zero, we can expect two real and unequal roots.

__Step 3 - take the square root of the discriminant Δ:__ √

Δ = √

(1920) √

Δ = 8√

30 __Step 4 - find numerator 1 which is -b + the square root of the Discriminant:__ Numerator 1 = -b + √

Δ Numerator 1 = -40 + 8√

30 __Step 5 - find numerator 2 which is -b - the square root of the Discriminant:__ Numerator 2 = -b - √

Δ Numerator 2 = -40 - 8√

30 __Step 6 - calculate your denominator which is 2a:__ Denominator = 2 * a

Denominator = 2 * -16

Denominator = -32

__Step 7 - you have everything you need to solve. 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 = | 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

__As a solution set, our answers would be:__(Solution 1, Solution 2) = ((-5 . 1√30)/-4, (-5 - 1√30)/-4)

### What is the Answer?

(Solution 1, Solution 2) = ((-5 . 1√30)/-4, (-5 - 1√30)/-4)

### How does the Projectile Motion Calculator work?

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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