A ball is thrown horizontally from a height h above the ground and hits the grou

Question

A ball is thrown horizontally from a height h above the ground and hits the ground with a speed that is n times its initial speed.

Derive a formula for the initial speed v0.

Remember: your final answer cannot have any variables in it except for h and n!

Be sure to specify clearly, with a drawing and a few words, what coordinate system you have chosen, where the origin is, and which directions you have chosen as positive. An algebraic formula, as opposed to a numerical answer, is one which contains symbols (such as g) instead of numbers with units (such as 9.8 m/s2). Dimensionless numbers such as ? or

Explanation / Answer

------>..Vx ............ .................. ....................... ........................... ............................V = 3Vx As it strikes the ground: ... ..........I ..............I..Vy=3VxsinQ ..............I ..........Q..I .Vx-------->V Vx = unknown..and here the angle is another unknown, so look for the method without the angle being used.....Here is the Force Diagram: .I.. .I..... .I...........3Vx .I............. V.----------->Vx Vy From Phythagorean Theorem ........h^2 = b^2 + a^2 (3Vx)^2 = (Vx)^2 + (Vy)^2 (Vy)^2 = (3Vx)^2 - (Vx)^2 ............= 9 (Vx)^2 - (Vx)^2 ............= 8 (Vx)^2 From free fall motion 2as = Vf^2 + Vi^2..

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