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# Trajectory Formula

Projectile motion is something that a body undergoes when it is thrown in air. The path taken by the projectile motion is called trajectory. A bomb released from an aeroplane in level flight, bullet getting fired from gun, an athlete throws a javelin illustrates the trajectory motion.

Trajectory formula is given by
Where,
y is the horizontal component,
x is the vertical component,
g= gravity value,
v= initial velocity,
$\theta$ = angle of inclination of the initial velocity from horizontal axis,

Trajectory related equations are
Where,
Vo is the initial Velocity,
sin $\theta$ is the y-axis vertical component ,
cos $\theta$ is the x-axis horizontal component.

 Related Calculators Trajectory Calculator Projectile Trajectory Calculator Acceleration Formula Calculator Area of a Circle Formula Calculator

## Trajectory Examples

Lets see some examples on trajectory:

### Solved Examples

Question 1: Lily throws a ball at an angle of 60o. If it moves at the rate of 5m/s and joe catches it after 3s. Calculate the vertical distance covered by it.
Solution:

Given: $\theta$ = 60o, initial velocity vo = 5m/s, time t = 3s,
The horizontal distance is given by
x = vxo t = 5m/s $\times$ 3s
x = 15 m/s2
y = x tan $\theta$ - $\frac{gx^2}{2v^2 cos^2 \theta}$

= x tan $\theta$ - $\frac{gx^2}{2v^2 cos^2 \theta}$

= 15 m/s2 tan 60o - $\frac{9.8 m/s^2 (15 m/s^2)^2}{2 (5m/s)^2 cos^2 60^{o}}$

= 22.4 m.

Question 2: Calculate the the range of projectile if initial velocity is 10 m/s and body is projected at 30o.

Solution:

Initial velocity vo = 10 m/s, angle of inclination $\theta$ = 30o

The range of a projectile is given by
R = $\frac{v_o^2 sin 2 \theta}{g}$

= $\frac{(10m/s)^2 sin 60^o}{9.8 m/s^2}$

= $\frac{(100 m^2/s^2 \times 0.866}{9.8 m/s^2}$

= 8.836 m.

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