Enter projectile motion problem
Solve the following projectile motion problem
Projectile motion equation:
h(t) = -16t2 + vt + h where:
h = height, v = velocity, and t = time
Plug in our numbers
h(t) = -16t2 + ()t +
When does the object hit the ground:
Set h(t) = 0
-16t2 + t + = 0
Evaluate the quadratic
Only take positive values
since height cannot be negative
Quadratic Formula
| = | -b ± √b2 - 4ac |
| 2a |
Calculate -b
-b = -()
-b = 0
Calculate the discriminant Δ
Δ = b2 - 4ac:
Δ = 2 - 4 x -16 x
Δ = 0 - 0
Δ = 0 <--- Discriminant
Since Δ = 0, we expect one real root.
Take the square root of Δ
√Δ = √(0)
√Δ = (0±√0)/
-b + Δ:
Numerator 1 = -b + √Δ
Numerator 1 = 0 + √0
-b - Δ:
Numerator 2 = -b - √Δ
Numerator 2 = 0 - √0
Calculate 2a
Denominator = 2 * a
Denominator = 2 * -16
Denominator = -32
Find Solutions
| Solution 1 = | Numerator 1 |
| Denominator |
| Solution 1 = | 0 |
| -32 |
Solution 1 = -0
Solution 2
| Solution 2 = | Numerator 2 |
| Denominator |
| Solution 2 = | 0 |
| -32 |
Solution 2 = -0
Solution Set
(Solution 1, Solution 2) = (-0, -0)
Prove our first answer
(-0)2(-0) ? 0
(0) + 00 ? 0
-0 + 00 ? 0
0 = 0
Prove our second answer
(-0)2(-0) ? 0
(0) + 00 ? 0
-0 + 00 ? 0
0 = 0
(Solution 1, Solution 2) = (-0, -0)
Keep Practicing
What is the Answer?
(Solution 1, Solution 2) = (-0, -0)
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.
This calculator has 1 input.
What 1 formula is used for the Projectile Motion Calculator?
h(t) = -16t2 + vt + h where:
h = height, v = velocity, and t = time
For more math formulas, check out our Formula Dossier
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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