## Projectile Motion Calculator :

Enter the projectile motion calculator its calculate the Initial velocity (V) in m/s, Angle of launch (α) in degrees(deg), Initial height (h) in meters(m), Time of flight (t) in seconds(sec), Distance (d) in meters(m), Maximum height (hmax) in meters(m), and you get the calculation below the calculator.

## Projectile Motion Formula :

Projectile motion is horizontal distance x is equal to the v_{x0(m/s)} in meter per second and multiply the time taken t_{ (s)} in second. Hence the projectile motion formula can be written as

**Horizontal distance ,x=v _{x0(m/s)}* t_{ (s)}**

**Horizontal velocity ,V _{x}=V_{x0}**

**Vertical distance y=V _{yo} t-1/2 gt^{2}**

**Vertical velocity, V _{y}=V_{yo}-gt**

Where,

V_{x} → velocity (along the x-axis)

v_{x0}→ initial velocity (along the x-axis)

V_{y} → velocity (along the y-axis)

V_{yo} → initial velocity (along the y-axis)

G → acceleration due to gravity in Newton/Kg-1

T → time taken in second

*Equations related to the projectile motion is given as,*

**Time of Flight t=2v _{0 }Sin θ/g**

**Maximum height reached H=VO ^{2} Sin^{2} θ /2g**

**Horizontal range R= VO ^{2} Sin 2 θ/g**

Where,

V_{0→} initial velocity s the initial velocity

Sin θ→ component along the y-axis

cos θ→ component along x- axis

The formula of projectile motion is used to calculate the velocity, distance and time observed in the projectile motion of the object

## Sample Examples :

### Example1 :

Johnson is standing on the top of the building and john is standing down. If Johnson tosses a ball with a velocity 50m/s and at the angle 40^{0} then at the 2s what height will the ball reach?

### Solution :

Given,

V_{yo} =50m/s

Δt=2s

The vertical velocity in the y direction is expressed as

V_{y}=V_{yo} Sin 40^{0}

V_{y}=50 sin 40

V_{y} =37.25m/s

### Example2 :

Johnson is standing on the top of the building and john is standing down. If Johnson tosses a ball with a velocity 80m/s and at the angle 50^{0} then at the 4s what height will the ball reach?

### Solution :

Given,

V_{yo} =80m/s

Δt=4s

The vertical velocity in the y direction is expressed as

V_{y}=V_{yo}* Sin 50^{0}

V_{y}=80 * sin 50^{0}

V_{y} =61.31m/s