Example 6: Impact Speed of a Projectile Hitting the Ground

Example 6: Impact Speed of a Projectile Hitting the Ground

From mes 3Speak Podcast by Math Easy Solutions

May 4, 2026

About this episode

This episode explores the impact speed of a projectile launched from a height, using parametric equations to calculate time, distance, and speed at impact.

https://3speak.tv/watch?v=mes/ae000ba6 In this video, I determine the time a projectile is in the air, the distance it travels, and the speed it impacts the ground after being launched from 10 meters at an angle of 45 degrees and a speed of 150 m/s. I use the parametric equations of trajectory I derived in my earlier video, and set the y component equal to zero to obtain the time when the object hits the ground. Plugging in that specific time value into the x component yields the distance. To get the velocity, we take the derivative of the position vector and then obtain the speed using the same time value, which is 151 m/s, which is similar to the launch speed. #math #vectors #calculus #physics #education Timestamps: Example 6: Find speed a projectile hits the ground – 0:00 Solution: Adjust the parametric equations of trajectory by adding the initial height of launch – 0:40 Plugging in our values into the parametric equations of trajectory – 3:56 Exact trigonometric ratios for π/4 – 6:33 Impact occurs when y = 0, which we can solve for t via the quadratic formula – 9:28 Distance is the x value at y = 0 – 15:03 Calculation check – 16:05 Velocity is the derivative of the position…

People in this episode

Host: Math Easy Solutions

Topics covered

  • projectile motion
  • impact speed
  • parametric equations
  • calculus
  • physics
  • education

Keywords

  • projectile
  • impact speed
  • trajectory
  • calculus
  • physics
  • velocity
  • trigonometric ratios

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