# physics

A football kicker can give the ball an initial speed of v_0 = 27.4 m/s. In order to score a field goal, the ball must go over the cross bar that is at a height of h = 3.44 m above the ground. If the kicker kicks the ball from a point d = 42.2 m from the goalposts, find the minimum and maximum angles at which he must kick the ball. Give the difference between the minimum and maximum.

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1. as you know, the height of the ball at distance x is

y(x) = tanθ x - 4.9/(v cosθ)^2 x^2

Using our data, we need to solve

42.2 tanθ - 4.9/(27.4 cosθ)^2 (42.2^2) = 3.44

42.2 tanθ - 4.9/(27.4^2 (1+tan^2θ))(42.2^2) = 3.44

I get tanθ = 1/3, but I don't get two values. At that speed the ball isn't going fast enough to cross the bar on its way up.

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2. In fact, I get that a Vi = 67 m/s is required if the ball is to be able to go over the bar at its max height, and more than that if we expect to have two values for θ.

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3. app really do be like that sometimes

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