# Maximum Height Calculator - Projectile Motion

**Created By :**
Sunil Kumar Gandipadala

**Reviewed By :**
Rajashekhar Valipishetty

**Last Updated :**
Apr 10, 2023

Maximum Height Calculator - Projectile Motion is a free online tool that computes the maximum height of the projectile. It takes velocity, initial height and angle of launch as input and produces the projectile maximum height in a fraction of seconds.

**Ex:** 10, 167, 48, 34.5 or 90

### How to Calculate Maximum Height of a Projectile?

The following are the simple and easy steps to evaluate projectile maximum height. Go through these steps and follow them carefully.

- Get the initial velocity of the object.
- the angle of launch and initial height of the object from the given question.
- Square the initial velocity, find the sine of angle square and multiply them.
- Double the acceleration due to gravity which is 9.81.
- Divide the result obtained in step 3 by step 4.
- Add the result to the initial height.
- The obtained result is called the maximum height of the projectile motion.

### FAQ's on Projectile Motion Maximum Height Calculator

**1. How to get maximum height in projectile motion?**

The simple formula to calculate the projectile motion maximum height is h + Vo/sub>² * sin(α)² / (2 * g). Students have to obtain the angle of launch, initial velocity, initial height and substitute those in the given formula. Evaluate the expression to get the maximum height of the projectile motion.

**2. Does height matter in projectile motion?**

Yes, the height of the object affects the trajectory of the projectile. For any speed of release, angle of release, the horizontal displacement increases as the height of release increases.

**3. How do you find the projectile maximum height on a calculator?**

Students have to enter data in the required input fields of the Maximum height calculator -projectile motion such as initial height, angle of launch, initial velocity. Hit on the calculate button to get the maximum height as output in the fraction of seconds.

**4. What is projectile motion?**

ProjectileA means an object which is flight after thrown or projected into the air. In projectile motion, the only acceleration acting is in the vertical direction and that is the acceleration due to gravity. Examples are football, baseball, cricket ball and so on.

### Maximum Height of Projectile Motion - Formulas

when a body is thrown or projected into the air, diagonally near the earth surface then it moves along the curved path of constant acceleration directed towards the centre of the earth. The path of that object is called the projectile motion.

The maximum height of the projectile is when that projectile reaches 0 vertical velocity. So, the vertical component of the velocity vector will point downwards. The horizontal displacement of the projectile is the range of the projectile and it depends on the initial velocity of the object.

When the object is launch from the ground (initial height = 0)

hmax = Vo² * sin(α)² / (2 * g)

When the object is launch from an elevation (initial height > 0)

hmax = h + Vo² * sin(α)² / (2 * g)

Where:

Vo is the initial velocity

α is the angle of launch

h is the initial height

hmax is the maximum height

**Example**

**Question: A firefighter plane aims a fire hose upward, toward a fire in a skyscraper. The water leaving the hose with a velocity of 38 m/sec. If the fire fighter holds the hose with an angle of 58.5°. Calculate the maximum height of the water stream.**

**Solution:**

The water droplet leaving the hose is considered as the object in projectile motion.

Initial velocity Vo = 38 m/sec

angle of launch α = 58.5°

acceleration due to gravity g = 9.8 m/sec²

Maximum height hmax = Vo² * sin(α)² / (2 * g)

= ((38)² x sin58.5°)/(2 x 9.8)

= (1444 x 0.852)/(19.6)

= 1230.288/19.6

= 62.76

Therefore, the maximum height of the water from the hose will be 62.76 m.

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