A basketball is thrown with an initial velocity v_ = (5.0, 7.5) m/s. The + y -di

Question

A basketball is thrown with an initial velocity v_ = (5.0, 7.5) m/s. The + y -direction is vertically upward, and the + x -direction is horizontal and downrange (toward the hoop). (Neglect the large size of the bal - assume that it is a small point mass located at the basketball's center. Neglect air resistance.) The is launched from an unknown initial height It arcs through the air, and 1.3 seconds later, it passes (at a somewhat downward angle) through the hoop at a height y = 3.0 m. From what initial height is the ball thrown? A. 1.2 m B. 1.5 m C. 1.8 m D. 2.1 m E. 2.4 m What is the player's horizontal distance from the hoop? A. 6.5 m B. 7.7 m C. 9.0 m D. 11 m E. 13 m. What is the magnitude of v_0? A. 6.5 m/s. B. 7.7 m/s C. 9.0 m/s D. 11m/s E.13 m/s What is the direction of v_0 (above the horizontal)? A. 56 degree B. 58 degree C. 61 degree D. 63 degree E. 65 degree Which one of the following statements about the basketball's motion is TRUE? A. The ball's (total) speed is zero at the top of its are B. The ball's acceleration is zero at the top of its arc. C. The ball's (total) speed decreases during ascent, and increases during descent. D. The ball's acceleration decreases during ascent, and increases during descent. E. The ball's acceleration is upward during ascent, and downward during descent. A gain, which one of the following statements about the basketball's motion is TRUE? A. The ball's acceleration depends on its mass. B. The ball's path through space is a segment of a circle. C. The ball's kinetic energy increases during ascent, and decreases during descent. D. The ball's potential energy increases during ascent, and decreases during descent. E. The ball's total mechanical energy increases during ascent, and decreases during descent. The Four Fundamental Forces of Nature are .. A. Galilean, Keplerian, Newtonian, Maxwellian B. Weight, Normal, Tension, Friction C. Weight, Lift, Thrust, Drag D. Gravitation, Electromagnetism, Nuclear Strong Force, Nuclear Weak Force E. The Jedi Force, The Fifth Element, Duct Tape, One Ring to Bind Them All

Explanation / Answer

10. Inital vertical vel = 7.5 m/s

                   hor. vel = 5.0 m/s

     time of ascent = v/g = 7.5/9.8 = 0.765 s

     total time of flight = 1.3 s

    time of descent =   1.3 - 0.765 = 0.535 s

maximum height reached from launch point = v2 /2g = 7.52/2*9.8 = 2.87 m

height desceded = gt2/2 = 9.8*0.5352/2 = 1.4 m

yo + 2.87 - 1.4 = 3

yo = 1.5 m (B)

11. horizontal vel = 5 m/s

     time of flight t = 1.3 s

horizontal distance x = 5*1.3 = 6.5 m (A)

12. magnitude Vel = sqrt(52 +7.52) = 9.01 m/s (C)

13. direction Tan(p) = 7.5/5 = 1.5

p = 56.31 deg, from th horizontal

14. (C) - The acceleration g is down ward , hecne the vel decreases during ascent and decreases during descent

15) (D) - potential enrgy is mgh, as height increases pote. energy increases.

16)

   

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