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A marble rolls along a level table that is 1.5 m above the floor. It has a constant velocity of 10 m/s. a)...

4) A marble rolls along a level table that is 1.5 m above the floor. It has a constant velocity of 10 m/s.
a) Once the ball leaves the table, calculate how long it will take for the ball to hit the floor.
b) Using the time you have calculated in part a, where would students place a cup to catch the marble when it hits the ground?
c) Suppose the table was doubled in height to 3 m. Determine the horizontal range (distance) of the marble as it falls to the floor. Hint: it's just double your answer from part b.
5) A 46-gram golf ball is launched with a velocity of 60 m/s at an angle of 35 degrees above the horizontal.
a) Calculate the horizontal and vertical velocities of the ball as it is launched. Answer: vx = ____ m/s
b) What is the acceleration of the ball 1.2 seconds after it is launched?
6) A kickoff sends a football with an initial velocity of 25 m/s at an angle of 50 degrees above horizontal.
a) On the axes to the right, sketch a line representing the relationship between the horizontal displacement of the football and the time the football is in the air. Sketch another line representing the vertical displacement of the football vs. time. Please label the two lines.
b) Find the x and y-components of the velocity
c) Find the time the ball is in the air. Answer: 3.83 seconds
d) Find the horizontal distance the ball travels before hitting the ground.
e) Find the maximum height of the ball.

Answer

  1. a) Use the formula for free fall: t = √(2h/g), where h = 1.5 m and g = 9.81 m/s².

    t = √(2 * 1.5 / 9.81) ≈ 0.553 seconds

  2. b) Horizontal distance = velocity * time = 10 m/s * 0.553 s = 5.53 meters.

    Place the cup 5.53 meters from the edge of the table.

  3. c) If the height is doubled to 3 m, the time is √(2 * 3 / 9.81) ≈ 0.782 seconds.

    Horizontal distance = 10 m/s * 0.782 s = 7.82 meters.

  4. 5a) Horizontal velocity, vx = 60 * cos(35°) ≈ 49.15 m/s. Vertical velocity, vy = 60 * sin(35°) ≈ 34.36 m/s.
  5. 5b) The acceleration of the ball is due to gravity, which is 9.81 m/s² downward.
  6. 6a) Sketch not possible in text format.
  7. 6b) vx = 25 * cos(50°) ≈ 16.07 m/s, vy = 25 * sin(50°) ≈ 19.15 m/s.
  8. 6c) Given as 3.83 seconds.
  9. 6d) Horizontal distance = vx * time = 16.07 m/s * 3.83 s ≈ 61.51 meters.
  10. 6e) Maximum height = (vy²) / (2 * g) = (19.15²) / (2 * 9.81) ≈ 18.68 meters.

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