23.03.2023 - 04:01

You are trying to throw a ball straight up to knock a Frisbee out of a tree. On your first throw, the ball makes it halfway up (from your hand to the Frisbee). To just barely make it to the Frisbee, your second throw needs to be ____ as fast as the first

Question:

You are trying to throw a ball straight up to knock a Frisbee out of a tree. On your first throw, the ball makes it halfway up (from your hand to the Frisbee). To just barely make it to the Frisbee, your second throw needs to be _____ as fast as the first throw.

Answers (1)
  • GAT
    April 9, 2023 в 07:44

    To determine how much faster the second throw needs to be, we need to consider the physics of projectile motion. When you throw a ball straight up, it experiences an initial upward velocity from your throw, but is then slowed down by the force of gravity as it rises. At the highest point of its trajectory (the halfway point), the ball momentarily stops and then begins to fall back down, accelerating due to the force of gravity.

    To knock the Frisbee out of the tree, the ball needs to reach the height of the Frisbee at the same time that the Frisbee is passing through that height. Since the Frisbee is stationary (not moving up or down), we can assume that it is at a fixed height.

    Since the ball takes the same amount of time to reach the halfway point on both throws (assuming the throws are made with the same initial velocity), the second throw needs to have a greater initial velocity to make it to the Frisbee. In fact, the second throw needs to be twice as fast as the first throw, because the time it takes to reach the Frisbee is the same as the time it takes to reach the halfway point (assuming negligible air resistance).

    Therefore, the answer is that the second throw needs to be twice as fast as the first throw to just barely make it to the Frisbee.

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