Problems Plus 2: Firing a Projectile Up and Down an Inclined Plane
In this video, I go over projectile motion along an inclined plane and show that the launch angle that gives the maximum range upwards or downwards is half the angle between the plane and the vertical. Even when firing at a target up an inclined plane, the angle that minimizes the energy used is also half the angle between the plane and the vertical. This result matches for a flat plane, since the maximum distance is achieved for a launch angle of 45°, i.e. half the angle between the plane (0°) and the vertical (90°).
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https://mes.fm/problems-plus-2-projectile-inclined-plane