# PROJECTILE MOTION CALCULATOR

Projectile motion calculator calculates the initial velocity (V0), initial angle (α), flight duration (t), horizontal distance (or range) (l) and maximum height (h) of a projectile motion in physics. The effect of air resistance is ignored.

## Projectile Motion Calculator

Formulas used in the projectile motion calculator are given below.

## Projectile Motion Formulas

If the initial velocity (V0) and angle (α) parameters are known;

$$l=\frac { { { V }_{ 0 } }^{ 2 }\sin { 2\alpha } }{ g }$$
$$h=\frac { { { { (V }_{ 0 } }\sin { \alpha } ) }^{ 2 } }{ 2g }$$
$$t=\frac { 2V\sin { \alpha } }{ g }$$

If the initial velocity(V0) and flight duration (t) parameters are known;

$$l=\sqrt { { { V }_{ 0 } }^{ 2 }-{ (\frac { gt }{ 2 } ) }^{ 2 } } t$$
$$h=\frac { g{ t }^{ 2 } }{ 8 }$$
$$\alpha =\tan ^{ -1 }{ \frac { 4h }{ l } }$$

If the initial velocity(V0) and maximum height (h) parameters are known;

$$\alpha =\arcsin { \frac { \sqrt { 2gh } }{ { V }_{ 0 } } }$$
$$l=\frac { { { V }_{ 0 } }^{ 2 }\sin { 2\alpha } }{ g }$$
$$t=\frac { 2V\sin { \alpha } }{ g }$$

If the maximum height (h) and travel distance (l) parameters are known;

$${ V }_{ 0 }=\frac { \sqrt { 2gh } }{ \sin { \alpha } }$$
$$\alpha =\tan ^{ -1 }{ \frac { 4h }{ l } }$$
$$t=2\sqrt { \frac { 2h }{ g } }$$

If the flight duration (t) and travel distance (l) parameters are known;

$${ V }_{ 0 }=\sqrt { { (\frac { l }{ t } ) }^{ 2 }+{ (\frac { gt }{ 2 } ) }^{ 2 } }$$
$$\alpha =\tan ^{ -1 }{ \frac { g{ t }^{ 2 } }{ 2l } }$$
$$h=\frac { g{ t }^{ 2 } }{ 8 }$$