Text Solution
Solution : As the horizontal velocity does not affect thevertical motion and initial vertical velocity of bothe the ball is zero, so both the balls will be reaching the ground simultaneously, i.e., <br> ` t_(1) =t_(2) = sqrt 2 h //g` <br> Velocity of the ball dropped vertically while reaching the ground is <br> ` v_(1) = sqrt 2 gh ` <br> For the ball projected horizontally, the horizontal component velocity ` v_(h_(2) =u and ` <br> vertical component velocity, ` v_(2) =sqer 2 gh`. <br> So the total v elocity of ball <br> ` v_(2) =sqrt( v_(H)_(2)^(2) + vv_(V)_(2)^(2) ) = sqrt (u^(2) + 2 gh)`<br> which is greater than ` v_(1)`. <br> It means the ball projected horizontally will strike the ground, with more speed than the ball dorpped vertically downwards.
Ball shot horizontally, one dropped vertically; both hit the ground at the same time.
What it shows:
The horizontal and vertical motions of a projectile are independent of each other. So two objects falling under the influence of gravity from the same height will reach the ground simultaneously, regardless of their horizontal velocities.
How it works:
The device, constructed by Nils Sorensen, consists of a spring loaded rod that shoots one of two billiard balls horizontally (pin-ball machine fashion). The second ball has a hole through it so that it slips over the other end of the rod. As the rod is released to fire ball #1, it slips out through ball #2 which then falls to the ground.
Setting it up:
The device clamps to a bench but protrudes over the edge giving the balls freedom of movement. A hard floor is vital here, because the best way to judge whether the balls strike the ground simultaneously is to listen for one or two cracks as the billiard balls land.
Simultaneously , a ball is thrown upwards and another dropped from rest. Which one hits the ground moving faster?
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The ball thrown upwards because during it's descent as it starts to fall back down it's velocity is increasing due to acceleration from gravity hence the greater the distance the greater velocity it will achieve before hitting the ground
Can someone please give me a detailed explanation on this?
Answers and Replies
well, really its velocity is changing by 9.8m/s every second. so the velocity is not necessarily increasing.
Also, about the problem generally, we are not supposed to just give you the answer on this forum. But we can help. My advice is to think about energy. Start thinking of things you know about energy in this situation.
Changing is what I meant , how does energy relate to this question? It is to do with projectiles , are you referring to kinetic energy of the ball?
Simultaneously , a ball is thrown upwards and another dropped from rest. Which one hits the ground moving faster?
-
The ball thrown upwards because during it's descent as it starts to fall back down it's velocity is increasing due to acceleration from gravity hence the greater the distance the greater velocity it will achieve before hitting the ground
Can someone please give me a detailed explanation on this?
In addition to thinking about the energies involved, you can also ask yourself what the velocity of the thrown ball will be when it passes you on the way down. Is it moving faster at that point than the ball that you dropped?
Changing is what I meant , how does energy relate to this question? It is to do with projectiles , are you referring to kinetic energy of the ball?
As for the equation, use the kinematic equation of motion for constant acceleration (gravity's acceleration is constant for this problem) -- use the one that relates the final velocity to initial velocity and acceleration, and the one that relates final position to initial position, velocity and acceleration...
Yes, the ball has kinetic energy and one other kind of energy. I was hinting about energy, because I think your teacher will be more happy if you give an explanation using the concept of energy. Your answer: "The ball thrown upwards because during it's descent as it starts to fall back down it's velocity is increasing due to acceleration from gravity hence the greater the distance the greater velocity it will achieve before hitting the ground" Is true, but not very qualitative. A better answer would be to say something definite about the difference in kinetic energy of the two balls when they hit the ground.
Edit: I meant to say quantitative, not qualitative. Those two are easy to get mixed up :)
I'm positive that the velocity of the ball that was thrown up on its way down will be greater than the ball that was dropped from rest but another person who I posed this question says otherwise that both balls would hit the ground with the same velocity since acceleration is constant for both balls regardless of the height it was dropped from or thrown up
So it is the ball thrown up then? Could anyone explain why relating to projectiles because we haven't covered energy in my class yet so It must be to do with velocity and acceleration
So it is the ball thrown up then? Could anyone explain why relating to projectiles because we haven't covered energy in my class yet so It must be to do with velocity and acceleration
ehild
ehild has the correct explanation as far as avoiding energy explanations. Here's an alternative, though: Isn't it true that if you throw a ball in the air that, by the time it falls to the same height you threw it from, it has the same speed (just in a different direction)? You should see that this is true just from the symmetry of the parabolic trajectory.
Now, consider the limiting case of the balls being released from a small distance above the ground.
So it is the ball thrown up then? Could anyone explain why relating to projectiles because we haven't covered energy in my class yet so It must be to do with velocity and acceleration