a ball is dropped from rest from the top of a cliff that is 24 m high. From ground level, a second ball is thrown straight upward at the same instant that the first ball is dropped. The initial speed of teh second ball is exactly the same as that with which the first ball eventually hits the ground. In the absence of air resistance, the motions of the balls are just the reverse of each other. Determine how far below the top of the cliff the balls cross paths.
2007-05-28 09:58:43 · 3 answers · asked by wildcherrychica1 2 in Science & Mathematics ➔ Physics
The 1st ball starts at rest and its speed increases as it falls. The 2nd ball starts with max speed and comes to a stop when it reaches altitude of 24 m. Ignoring direction of the speed, both balls have identical speeds at all points along their paths.
Divide their trips in 2, above passing point and below passing point. The above portion for both is the portion which is traveled with lower speeds.
We can also divide the time in 2 portions. The 1st ball travels the upper, slow, portion during the time that the 2nd ball travels the lower, fast, portion. The 2nd ball travels the equivalent (but reversed) path in the 2nd time period. The time for the 1st ball to travel its upper portion must be equal to the 2nd ball's time for the upper portion. The 2nd ball travels the upper portion after passing the other ball. So they must pass after 1/2 the total time has expired.
Total time:
y = (1/2)*g*t^2
solve for t, total time.
Calculate how far the first ball fell in 1/2 that time.
2007-05-28 13:52:30 · answer #1 · answered by sojsail 7 · 0⤊ 0⤋
The ball thrown downward would hit the ground first because it has the largest negative vertical velocity. The that is dropped and the ball thrown horizontally both only have gravitational acceleration pulling them down in the vertical direction, so they hit at the same time. Then the ball thrown upwards hits last since it is given a velocity in the positive vertical direction to counteract the negative gravitational force.
2016-04-01 01:24:51 · answer #2 · answered by Karen 4 · 0⤊ 0⤋
they will cross paths at the centre of the cliff or 12 meter,.
2007-05-28 10:02:30 · answer #3 · answered by martinpaul2001 3 · 0⤊ 0⤋