MAT 21C Lecture Notes - Lecture 17: Projectile Motion, Scalar Multiplication, Cross Product
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MAT 21C Full Course Notes
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Announcements: hw6 due 11/2, midterm 2 11/4. Newton"s second law of motion: force acting on projectile is equal to the projectile"s mass times its acceleration. If the force acting on a projectile is only gravitaional force = mg ~j , then m d2 ~r dt2 = mg ~j and d2r dt2 = g ~j. Solve the initial value problem dt = ( gt) ~j + ~v0 dt ~r = ~v0 when t = 0. 2 gt2 ~j + ~v0 t + ~r0 dt2 = gj initial condition: ~r = ~r0 and d di erential equation: d2 ~r. For ideal projectile motion, when an object is launched from the origin nover a horizontal surface with initial velocity ~v0 and launch angle : maximum height: ymax = (| ~v0 | sin )2. Ight time: t = 2| ~v0 | sin range: r = | ~v0 |2.
