Bob punts a football 1m above the ground, at an angle of 37° with respect to the horizontal direction. Alice is 50m from Bob and starts to r

Question

Bob punts a football 1m above the ground, at an angle of 37° with respect to the horizontal direction. Alice is 50m from Bob and starts to run towards the ball when the ball is kicked. The initial speed of the ball is 20m/s.

Required:
Determine the minimum speed of Alice so that she can make the catch before the ball hits the ground.

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Đan Thu 2 days 2021-07-22T01:32:01+00:00 1 Answers 0 views 0

Answers ( )

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    2021-07-22T01:33:53+00:00

    Answer:

    The value is v  =  3.75 \  m/s

    Explanation:

    From the question we are told that

    The height of the ball above the ground is h  =  1 \  m

    The angle is \theta =  37 ^o

    The distance of Alice from Bob is d = 50 m

    The initial speed of ball is u = 20 m/s

    Generally the height of the ball is mathematically represented as

    h  =  -u sin(\theta)t +  \frac{1}{2} (g) t^2

    => 1  =  -20 sin(37)t +  \frac{1}{2} * 9.8 t^2

    => 1  =  -12t + 4.9 t^2

    =>  4.9 t^2  - 12t  -1  = 0

    using quadratic formula we have that

    t  =  2.536 \  s

    The other value of time obtained is negative so we would not consider it as time can not be negative

    Generally the distance the ball traveled in the horizontal direction is

    s =  ucos(\theta ) * t

    => s =  20 *  cos (37 )* 2.536

    => s = 40.5 \  m

    Generally the distance that Alice will travel before she get to the ball is

    L  =  d  -  s

    => L  =  50 - 40.5

    => L  =  9.5 \ m

    Generally the minimum speed of Alice is mathematically represented as

    v  =  \frac{  9.5}{ 2.536}

    v  =  3.75 \  m/s

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