Example 6: Impact Speed of a Projectile Hitting the Ground

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 vector – 18:26
• Speed at impact is 151 m/s – 21:10
• Calculation check – 22:50 .

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