Anonymous
Anonymous asked in Science & MathematicsPhysics · 1 month ago

Kinematics help please!?

A basketball player scores a three point shot form the three point line, which is 7.24 meters from the hoop. The ball was thrown from a height of 2.00 meters above the court at an angle of 45 degrees. The hoop is 3.00 meters above the court and air resistance can be ignored.

a) What speed was the ball thrown at?

b) How long did the ball take to reach the hoop?

c) What were the ball's velocity components when it reached the hoop?

2 Answers

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  • Ash
    Lv 7
    1 month ago
    Favorite Answer

    Let u = initial velocity f the ball, 

    then horizontal component, ux = ucos45 =  u/√2

    and vertical component, uy = usin45 = u/√2

    Horizontal travel of ball 

    d = (ux)t

    7.24 =  ut/√2  .....(1)

    Vertical travel of the ball

     s = (uy) t + ½gt²

    (3.00 - 2.00) = ut/√2 + ½(-9.81)t²

    1.00 =  ut/√2 - 4.905t²

    plug in from (1)

    1 = 7.24 - 4.905t²

    4.905t² = 6.24

    t = 1.13 s

    From (1)

    u = (7.24√2)/t

    u = (7.24√2)/(1.13)

    u = 9.06 m/s

    vertical component of velocity when ball reaches the hoop = vy

    vy = uy+at

    vy = (u/√2) + (-9.8)(1.13)

    vy = (9.06/√2 ) - (9.8)(1.13)

    vy = -4.67 m/s  ( 4.67 m/s downwards)

    horizontal component of velocity when ball reaches the hoop = vx

    vx = ux = u/√2 = 9.06/√2 = 6.41 m/s

    Answers

    (a) Speed at which ball was thrown : 9.06 m/s

    (b) Time to reach the hoop : 1.13 s

    (c)  Ball's velocity component at the hoop:

          horizontal : 6.41 m/s

         vertical : 4.67 downwards

  • oubaas
    Lv 7
    1 month ago

    since the angle is 45°, then both sine e cosine are worth 0.707

    vertical motion equation 

    (3-2) = Vo*0.707*t-4.903*t^2  (1)

    horizontal motion equation

    7.24 = Vo*0.707*t   (2)

    t = 7.24 / (Vo*0.707)

    back to equation (1) :

    1 = Vo*0.707*7.24 / (Vo*0.707) - 4.903*7.24^2/(0.5*Vo^2)

    257/(0.5V^2) = 6.24

    257 = 3.12Vo^2

    Vo = √ 257/3.12 = 9.08 m/sec

    t = 7.24/(9.08*0.707) = 1.128 sec 

    tup = Vo*0.707/g = 9.08*0.707/9.806 = 0.655 sec 

    t down = t-tup= 1.128 - 0.655 = 0.473 sec 

    Vdown = g*t down = 0.473*-9,806 = -4.64 m/sec 

    Vx = Vo*0.707 = 9.08*0.707 = 6.42 m/sec 

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