### Equation of the Path of a Projectile

Different equations used in projectile motion to calculate time of flight, horizontal range, maximum height etc.

Let
O = Point of projection,
u = Velocity of projection, and
Î± = Angle of projection with the horizontal.

Consider a point P as the position of particle, after time t seconds with x and y as co-ordinates, as shown in Fig. 1.30.

The equation of the path of a projectile or the equation of trajectory is given by

Since this is the equation of a parabola, therefore, the path traced by a projectile is a parabola. The following are the important equations used in projectiles:

1. The time of flight (t) of a projectile on a horizontal plane is given by

2. The horizontal range (R) of a projectile is given by

For a given velocity of projectile, the range will be maximum when sin 2Î± = 1 or Î±=45.

3. The maximum height (H) of a projectile on a horizontal plane is given by

4. The time of flight of a projectile when it is projected from O on an upward inclined plane as shown in Fig. 1.31, is given by

where Î² is the inclination of plane OA with the horizontal.

When the projectile is projected on a downward inclined plane, then

5. The range of projectile when it is projected from O to B on an upward inclined plane, as shown in Fig: 1.31, is given by

For a given velocity of projectile, the range will be maximum when

When the projectile is projected on a downward inclined plane, then

### Are Engineers Favourite Among Girls?

What do girls think about men who are engineers and what type of engineers are most favourite among girls? A survey was conducted by a team of aboutmech with members chosen from different countries. Each team member carried out a neutral survey in his/ her country to evaluate what females think about most of the engineers from different engineering branches. An overview of different questions asked in survey is given below: Question: Which male engineers do you find more attractive as a husband? Almost 50% women voted for mechanical engineers to be the most attractive husbands among other engineers. So mechanical engineers are most favourite among girls as a husband. They find them more trustworthy, intelligent, and creative. A married women from California said, “If your husband is a mechanical engineer, he will help you in everyday tasks. Because mechanical engineers are good team players and they have creative ideas about everything.” Which male engineers do you find more