aballistossedintotheairat40feetpersecondfromaheightof5feet.howlongwillittaketheballtoreachtheground

Enter Projectile Motion Problem

Set up the projectile motion equation:

h(t) = -16t2 + vt + h where:
h = height, v = velocity, and t = time

Plug in our numbers to the projectile motion equation:

h(t) = -16t2 + (40)t + 5

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

-16t2 + 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:
 = -b ± √b2 - 4ac 2a

Step 1 - calculate negative b:
-b = -(40)
-b = -40

Step 2 - calculate the discriminant Δ:
Δ = b2 - 4ac:
Δ = 402 - 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)

(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?

1. h(t) = -16t2 + 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