Dynamics Engineering Mechanics 2nd edition Gray Problem 2.104 A soccer player pr

Question

Dynamics Engineering Mechanics 2nd edition Gray Problem 2.104 A soccer player practices kicking a ball from A directly into the goal (i.e. the ball does not bounce first) while clearing a 6 ft tall fixed barrier. 2.104: Determine the minimum speed that the player needs to give the ball to accomplish the task. Hint: Consider the equation for the projectile's trajectory of the form y = C0 + C1X + C2X^2 with the y axis parallel to the direction of gravity, for the case in which the ball reaches the goal at its base. Solve this equation for the initial speed v0 as a function of the initial angle theta, and finally find v0 minimum as you learned in calculus. Don't forget to check whether or not the ball clears the barrier.

Thank you for your help!

Explanation / Answer

here time of flight = 2usin/g ( is the angle that velocity makes with horizontal)
now range = ucos*2usin/g = 58ft
or u^2sin2/g = 58 ft
this is the expression for velocity and angle f
for u to be minimum =45
so u= 58g = 43.08 ft/s

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