Which ball has the greatest final velocity?

Question

Three balls are thrown from a cliff. One is thrown straight up, One is thrown straight down, and one is thrown horizontally. Which ball has the greatest FINAL velocity?

Answer 1

If they are thrown with the same MAGNITUDE of velocity, and you are either not counting air resistance or are assuming that they all have the same drag parameters, then the MAGNITUDES of the final velocities will all be the same. The actual velocities of the ones thrown up and down will be exactly the same while the one thrown horizontally will have a horizontal component an a lesser vertical component. Still, all magnitudes will be the same.

If however, they are thrown at different speeds, then it will be the one that is thrown the hardest If you are counting air resistance and the balls have different drag parameters, then you have not provided enough info to tell.

And if by final velocity you mean after they have come to rest on the ground, then obviously they all have a velocity of 0. Typically this is not referred to as final though.

Answer 2

Not counting air resistance, if all are thrown with the same initial velocity in different directions, then the one thrown horizontally has a smaller final velocity than the other two, which have equal final velocities.

With air resistance, the ball thrown downward is in the air for less time, so air resistance has the least effect upon it and this ball has the greatest final velocity.

Answer 3

generally final velocity refers to the velocity right before the ball hits the ground, so it wouldnt be zero. it all the balls are thrown with the same force, then the ball thrown straight up and the one thrown down will have the same final velocity, while the one thrown horizontally will have less (because if you add one vector to another, it is longer than if you use pythagorean theorem to find the vector that is the sum of two perpendicular vectors) Therefore there are 2 right answers to this problem

Answer 4

I considered the problem using conservation of energy. The ball will lose potential energy from the fall starting at the point of the toss equal to m*g*h

it has a starting kinetic energy of 1/2 * m *v1^2

the final kinetic energy, in a frictionless world will be:
1/2 * m*v2^2
which must be equal to the sum of the potential energy lost and the starting kinetic energy. In this case all three have the same final velocity. However, the direction will be different for the ball thrown horizontally.

Considering friction, the energy lost to friction of the air is the force

1/2*C*p*A*v^2
where ρ is the air density, A the cross-sectional area, and C is a numerical drag coefficient

Assuming a constant for all three scenarios,
1/2*C*p*A*=k
then which is the least amount of loss due to air resistance?

Consider the forces on the ball:

gravity and air resistance.

for upward flight
dv/dt=-a-2kv

for downward flight
dv/dt=a-2kv

for horizontal flight
dv/dt =a-2kv

Based on the dynamics of flight, the ball thrown downward will have the least area under the time distance graph, so it has the least energy lost to drag and will have the highest final velocity.

Of course, eventually the balls strike the ground and will come to rest...


j

Answer 5

Easy answer... 0 if Final means after impact and all forces are at equilibrium...
But let's play.... Game on!
Assumptions:
1) Final Velocity vector is just before impact with the ground
2) All three balls have identical physical characteristics (mass, density, surface area...)
3) All three throwing forces are the same

4A) The "cliff" is very very short (not ignoring air friction)

*4B) Cliff is tall enough for all three balls to reach terminal velocity at the time of impact (not ignoring air friction)

**4C) Cliff is very very very tall (not ignoring air friction)

***4D) Or we ignore air friction and assume that the throwing force is equivalent in all three cases. (In this case, ignoring air friction, the height of the cliff does not matter.)

Under assumption 4A:
If the "cliff" is really really small the downward thrown ball will have the highest v vector

*4B:
The ball thrown horizontally will most likely have the largest velocity vector... (assuming that the time required to reach t v isn't enough to take out horizontal velocity.)

**4C:
Really super tall cliff. Horizontal vector will be cancelled by air friction leaving all three with equal terminal velocity

***4D:
All three balls will hit the ground with equal velocity vectors... Why: The cliff height gives all balls the same potential energy whereas the balls all have the same initial kinetic energy. Energy is conserved (if we ignore air resistance).

Answer 6

The ball with the greatest final velocity is the one that is thrown hardest.

Answer 7

Objects moving in different directions have different velocities. But when you ask for "greatest velocity", there's no way to take direction into account. "greatest velocity" would be equivalent to "greatest speed". Ignoring air resistance and assuming the initial speed of all three balls was the same, they will hit the ground at different times, but with the same speed at impact.

Answer 8

It depends upon the initial speeds of the balls thrown up and down. (The one launched horizontally will be slower than the other two.) If the ball thrown up is thrown with the same speed as the ball thrown down they will have the same velocity when they hit the ground... the one starting up will just be later! Whichever of the up or down balls which starts with the greater speed will have the greater speed at the ground.

Answer 9

Unanswerable until you give the initial velocities of the balls thrown up and down.

Answer 10

Considering all of the balls are the same weight and mass, I believe it would be the ball thrown straight up, however, I do not know because you left so many variables out.