Grade 12 Physics Problems

Discussion in 'Homework' started by Wyrm, Oct 21, 2010.

  1. Wyrm

    Wyrm Active Member

    I would appreciate it if someone could help me with the following problem.

    A ball is thrown at an angle of 45 degrees at a speed of 40m/s. Each time it bounces, it loses 75% of its speed. How far does it travel before it stops?

    What I don't understand is that because it only loses 75% of its speed, doesn't that mean it never stops?

    If someone could explain a solution to me, I'd be grateful.
  2. -Cirno

    -Cirno Well-Known Member

    geometric sequence...
  3. -Cirno

    -Cirno Well-Known Member

    and yeah, that question seems to lack more info...
  4. Shamanics

    Shamanics Banned

    The each time it bounces loses 75% of its speed is a data, depend on the floor material and the ball material.

    We decompose the speed in 2 speeds, one forward (->) and one up (/|).

    Each of these speeds is sqrt (2) * 20 (do the math).

    Now the ball accelerates downwards (|/) at 10m/s*s.
    So it takes sqrt (2) * 20/10 = sqrt (2) * 2 seconds to stop going up and start going down.
    In that time it moved sqrt (2) * 2 * sqrt (2) * 20 = 80m. (sqrt (2) * 2 = time, sqrt (2) * 20 = speed).
    Since it has constant acceleration it describes a parabola. We know the vertex is between both roots, so that means it hits the ground again at 160m.

    Now the next time, the speed will be 10m/s and the starting angle will be the same.

    This means it moves 160m * 1/4, or 40m. We can keep on like this forever since it will never stop, but we do realize that it moves always slower.

    So it moves

    160m * (1+1/4+1/4/4+1/4/4/4.................) = 160 * (1+1/4+1/16+1/64........)

    Now some math.

    1 + 1/x + 1/x2 + 1/x3 + 1/x4.... 1/xn + 1/x n+1) = 1 + 1/x-1. (this applies for all x > 1)

    So 160m * (1+1/4+1/4/4+1/4/4/4......................) = 160 * (1+1/4+1/16+1/64..........) = 160 * (1+1/3) = 160m * 4/3 = 640m/3.

    The ball moves 640m/3. Though it actually never stops.
  5. Wyrm

    Wyrm Active Member

  6. Night1301

    Night1301 Well-Known Member

    True, that is the closest answer, IMO, the question itself is wrong since the ball would literally never stop on a closed system (and we didn't deal with friction either)
  7. Kenshiro

    Kenshiro Well-Known Member

    Reminds me of one of my old physics problems, although I don't remember exactly how it was formulated. :)
  8. Punj.Love Hater

    Punj.Love Hater Well-Known Member

    Fuck, shamanics answered it again. Well he is 200% right. My all labour solving on my note-book went in vain.