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my dad said that a cannot throw a ball further from the third floor than from the the ground floor. That the hieght have no effect on the horizontal distance is this so and why.
- Anonymous (age 13)
Assume you throw the ball horizontally. There are two components to the velocity of the ball. The vertical component is affected by the force of gravity and increases linearly with time, starting from zero. The horizontal component continues with its same value until it hits the ground. Since the time the ball takes to hit the ground increases the higher up you are, the horizontal distance covered when it hits the ground is larger. So it goes farther. Note: we have neglected air resistance here but it will not affect the overall conclusion about greater distance the higher you are.
(published on 01/04/2010)
Follow-Up #1: throwing things
I believe you missed the point of the fatherís comment. If the kid can only throw the ball 30yds he will not be able to throw it further simply because he is higher. The force acting in the horizontal x-direction does not increase due to height.
Your answer, taken with the fatherís point, is that the lower one hits the ground sooner but if there is still kinetic force in the x-direction the ball will bounce and roll until it comes to a stop alongside the ball from the high height; disregarding the coefficient of friction of the grass.
A key lesson is if you cannot jump a distance x from the patio into the pool at ground level due not try it from the tenth story balcony.
I'm not sure how to put this delicately. You're 100% wrong.
No one said that the arm could exert more force higher up. The point is that the same horizontal velocity imparted higher up leads to longer travel before the ball hits. As for how far the balls roll after landing, if you disregard friction they roll forever. So I wouldn't disregard friction.
Your advice about not jumping off tenth story balconies is good, but as a matter of fact you can make it farther horizontally from there than from a patio, for the same reason we explained previously for ball-tosses.
(published on 01/13/10)
Follow-up on this answer.