Example 5: Horizontal Distance Traveled by a Projectile

Example 5: Horizontal Distance Traveled by a Projectile

From mes 3Speak Podcast by Math Easy Solutions

May 1, 2026

About this episode

This episode explores the calculation of horizontal distance traveled by a projectile launched at an angle, focusing on the integration of gravitational effects.

https://3speak.tv/watch?v=mes/8dbed9fa In this video, I determine the vector formula for path of a projectile launched at an angle by integrating the acceleration due to gravity acting on it, and then integrating its velocity vector. When the y-component of the position vector is equal to zero (i.e. the object strikes the ground), the corresponding non-trivial time variable corresponds to the horizontal distance traveled. This distance is maximized when the launch angle is π/4 radians or 45 degrees. #math #vectors #calculus #physics #education Timestamps: Example 5: Find angle that gives the maximum horizontal distance traveled by a projectile – 0:00 Solution: Gravity is the only force that acts on the object – 0:49 Integrate the acceleration due to gravity to get the velocity vector – 3:02 Integrate the velocity vector to obtain the position vector – 5:29 Components of the initial velocity – 8:04 Position vector and the parametric equations of trajectory – 11:00 The projectile follows the path of a parabola since y is a quadratic function of x – 13:39 Horizontal distance is the value of x when y = 0 – 16:23 Solving for the distance by plugging in the non-trivial t-value…

People in this episode

Host: Math Easy Solutions

Topics covered

  • projectile motion
  • calculus
  • vectors
  • physics
  • education

Keywords

  • projectile
  • horizontal distance
  • launch angle
  • gravity
  • integration

Mentioned in this episode

Books & works: Example 5: Horizontal Distance Traveled by a Projectile

Places: 3Speak, Hive

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