A soccer ball is kicked from <0,0,0> with Vo = <0,80,80> ft/s. The spin on the b

Question

A soccer ball is kicked from <0,0,0> with Vo = <0,80,80> ft/s.

The spin on the ball gives it an acceleration of <1.2,0,0> ft/s^2

a) Find the position and velocity vectors.

b) At what time does the ball hit the ground, and what is its position vector then?

c) Find the max height the ball achieves.

Can you show me how you solve the problem?

Much appreciated!

Explanation / Answer

a.) acceleration due to spin = ft/s^2 acceleration due to gravity = ft/s^2 Net acceleration = ft/s^2 Position vector S = u*t + (1/2)*a*t^2 = + ft/s^2 = Velocity vector V = u + a*t = + ft/s^2 = b.) Hit the ground => Sz=0 => 80*t-16.087*t^2 =0 => t = 4.97 sec S = = ft/sec^2 c.) Max height when Vz = 0 => 80-32.174*t = 0 => t = 2.485 sec Height = Sz = 80*t-16.087*t^2 = 99.42 ft

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