Lebron James and Stephen Curry are playing an intense game of minigolf. The final(18th) hole is 8.2 m away from the tee box (starting locati

Question

Lebron James and Stephen Curry are playing an intense game of minigolf. The final(18th) hole is 8.2 m away from the tee box (starting location) at an angle of 20◦ east of north. Lebron’s first shot lands 8.6 m away at an angle of 35.2◦ east of north and Steph’s first shot lands 6.1 m away at an angle of 20◦ east of north. Assume that the minigolf course is flat.
(A) Which ball lands closer to the hole?
(B) Each player sunk the ball on the second shot. At what angle did each player hit their ball to reach the hole?

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MichaelMet 4 years 2021-09-01T20:53:29+00:00 1 Answers 6 views 0

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  1. Maris
    0
    2021-09-01T20:54:55+00:00
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    Answer:

    A. we will see that the notion \mathbf{|r ^ \to - r_2 ^\to| = 2.10006 \ m} which denotes Stephen Curry  illustrates that Stephen Curry minigolf ball shot is closer

    B.  Lebron James hits at an angle of 17.48° North -East.

    The direction of Stephen is   = 20° due to East of North

    Explanation:

    Let r ^ {\to represent the position vector of the hole;

    Also; using  the origin as starting point. Let the east direction be along the positive x axis and the North direction  be + y axis

    Thus:

    r ^ {\to  = 8.2 \ sin 20^0 \hat i + 8.2 \ cos 20 \hat j

    r ^ {\to  = (2.8046 \hat i + 7.7055 \hat j ) m

    Let r_1 ^ \to be the position vector for Lebron James’s first shot

    So;

    r_1 ^ \to = (8.6 \ sin \ 35.2 )^0 \hat i + 8.6 \ cos \ ( 35.2)^0 \hat j

    r^ \to = (4.9573 \hat i + 7.02745 \hat j) m

    Let r_2 ^ \to be the position vector for Stephen Curry’s shot

    r_2 ^ \to  =6.1 \ sin 20^0 \hat i + 6.1 \ cos \ 20 \hat j

    r_2 ^ \to  = (2.0863 \hat i + 5.7321 \hat j )m

    However;

    r ^ \to - r_1 ^\to = (-2.1527 \hat i + 0.67805 \hat j) m

    \mathbf{|r ^ \to - r_1 ^\to| =2.25696 \ m }

    Also;

    r ^ \to - r_2 ^\to = (0.71013 \hat i - 1.9734 \hat j) m

    \mathbf{|r ^ \to - r_2 ^\to| = 2.10006 \ m}

    Thus; from above ; we will see that the notion \mathbf{|r ^ \to - r_2 ^\to| = 2.10006 \ m} which denotes Stephen Curry  illustrates that Stephen Curry minigolf ball shot is closer

    B .

    For Lebron James ;

    The angle can be determine using the trigonometric function:

    tan \theta = ( \dfrac{0.67805}{-2.1527}) \\ \\ tan \theta = -0.131498 \\ \\ \theta = tan ^{-1} ( -0.31498) \\ \\ \mathbf{\theta = -17.48^0}

    Thus  Lebron James hits at an angle of 17.48° North -East.

    For Stephen Curry;

    tan \theta = ( \dfrac{-1.9734}{0.7183}) \\ \\ tan \theta = -2.74732 \\ \\ \theta = tan ^{-1} ( -2.74732) \\ \\ \mathbf{\theta = -70.0^0}

    The direction of Stephen is  = 90° – 70° = 20° due to East of North

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