Cannon ball!

The iron ball has more mass and therefore more initial momentum, since the initial velocity is the same. The friction due to air will slow down both of the balls and reduces the momentum. The friction force is (approximately) the same for both balls, because it depends on the velocity and the size of the balls only. Therefore the change in the momentum, $\Delta p$ will be also the same. The corresponding change in the velocity will be $\Delta v=\Delta p/m$ that is larger when the mass is smaller. The rubber ball will have slightly less velocity and will travel to a shorter distance.

In reality, the friction forces are not exactly equal, because the rubber ball's velocity is slightly less than the iron ball's. This will not change the conclusion.

If there is no air, the two balls will travel exactly the same distance.

Both balls are accelerated to the same rate by the cannons, but since the steel is more massive, it decellerates by air resistance slower and thus travels farther

Given initial speed is u = 50 m/s . Since both the balls come to rest finally so final velocity for both the balls v = 0 . Now, mass of iron ball is more than rubber ball . Let the mass of iron ball be x and that of rubber ball be y such that x > y . Force produced on both the balls by the cannon is same . Let the force be F . And both the balls have different accelerations $a_1$ , $a_2$ because they are of different masses .

F = $m_1$ x $a_1$ $\Rightarrow$ $a_1$ = $\frac{F}{x}$

F = $m_2$ x $a_2$ $\Rightarrow$ $a_2$ = $\frac{F}{y}$

Now it is clear that acceleration of rubber ball ( $a_2$ ) is greater than acceleration of steel ball ( $a_1$ ) . But the balls are retarding so the acceleration will be negative , that is , a = -a .

From Kinematics : 2aS = $v^2$ + $u^2$

So now S = $\frac{0 - 2500}{2 x (-a)}$ = $\frac{1250}{a}$

Hence , $S_1$ = $\frac{1250}{a1}$ = $\frac{1250*x}{F}$

And , $S_2$ = $\frac{1250}{a2}$ = $\frac{1250*y}{F}$

Now , we will have the value of $S_2$ greater than $S_2$ (The reason is that the value of numerator is greater in $S_1$ than in $S_2$ because x is grater than y) . Therefore , the ball made of steel will travel to a longer distance .

Answer: Stella (the iron ball).

We know that the formula to find momentum is:

$\ p=\ mv$

where p is the momentum

m is mass $kg$

And v is the current velocity $m/s$ .

It is also handy to note that momentum $p$ can be measured in $kg$ x $m/s$ . $Also,$ ( $kg)(m/s)$ (which is the format I'm using) (they're the same thing).

(This basically means the distance the mass travels every second).

So, momentum is the measure of how far mass(e.g. (kg)) travels(e.g. meters) per a given time(e.g. seconds). We can take mass for an object, like a ball. Also, these are the most common units used for momentum, mass and velocity by far.

$Now$ $to$ $the$ $question:$

let the cannons shoot the 2 balls, each with a velocity of 50m/s.

First of all, we can instantly see that both balls are travelling the same angle (theta $(\theta)$ ) , so we don't have to worry about magnitude (direction).

Plus, the balls are being shot above ground, so we don't have to worry about impacts, until they hit the ground.

Furthermore, they are both the same size, so it isn't unfair in any way.

Now, from general knowledge (and science) we know the mass of the metal ball is greater than that of the rubber ball: as they are both the same size, and metal weighs more than rubber, with the same gravitational field strength(you could just say the gravitational field strength of earth) (By the way, this is because:

$weight$ $=$ $mass$ x $the$ $gravitational$ $field$ $strength$ ).

Therefore, the metal ball is heavier than the rubber ball (on earth), and therefore the metal ball has more mass than the rubber ball.

$Now,$ $to$ $the$ $actuall,$ $actuall$ $question:$

Now we know that the mass of the iron ball is greater than the mass of the rubber ball. ( $mass$ $of$ $iron$ $ball$ $>$ $mass$ $of$ $rubber$ $ball$ )

And they are both travelling at a velocity of $50m/s$

Using the formula: $\ p=\ mv$ , we can calculate the momentum

$...$

let the mass of the iron ball = $i$ , and let the mass of the rubber ball = $r$

the momentum of the iron ball = $i(kg)$ x $50(m/s)$

Which can be written as: $50i(kg)(m/s)$

$...$

the momentum of the rubber ball = $r(kg)$ x $50(m/s)$

Which can be written as: $50r(kg)(m/s)$

$i>r$ , so we can easily see that:

$50i(kg)(m/s)$ $>$ $50r(kg)(m/s)$

Therefore, $the$ $momentum$ $of$ $the$ $iron$ $ball$ $>$ $the$ $momentum$ $of$ $the$ $rubber$ $ball$

Now, remember... momentum measures how far mass(an object) travels per a given time. In this case, it is how far the mass travels (in meters) per second.

because the momentum of the iron ball is greater than that of the rubber ball, it will travel further per second (than the rubber ball), with it's first hit to the ground, further than the rubber ball.

Stella wins the competition, as she launched the iron ball.

Extra: The rubber ball may travel further overall, but ONLY after the first bounce. This is because rubber has lots of elastic potential energy (and therefore upthrust), when hitting the ground, to propel the ball even further. Basically meaning, it is bouncy.

Whereas, the rubber ball still generates more friction than the iron ball, so the iron ball may still have a moderate chance (if it is presumed not to be rough, which it usually isn't).

Furthermore, the metal ball may make up the distance the rubber ball used for propelling itself, by rolling.

Answer: Stella (the iron ball).

The way i did it is that kinetic energy is equal to the mass of the object multiplied by the velocity squared (KE= $\frac{1}{2}$ MV^2) so since we know the velocity is 50 meters per second, plus with the understanding that the balls are the same size, we know that the steel ball will have more mass due to its density being larger than the rubber ball. Knowing that the mass will be larger than the rubber ball, we know that the kinetic energy is larger therefore stating that it will go further.

Since Force=Mass x Acceleration and the force is the amount of power the ball will have, when the acceleration is constant, as in the example, the higher the mass, the more power the ball will have.

I imagine the scenario and I think that the rubber ball will be easier to be deformed and flattened out due to air resistance. But if that's not the case than the one with more mass will experience less air resistance and will win. This case it's the steel ball.

My answer was based on practical experience, I've experienced to bowl faster with a hard bowl than a rubber or cosco ball, with same effort. And that is how I deduced, the one which is heavier will travel farther.

If the balls are the same size then it's safe to state that the steel ball weighs more than the rubber ball. The steel ball will then travel further than the rubber ball because it generates more force.

E=mc^2. As per this equation the object having more mass travels at high speed.

Heavy objects travel further than rubber because of the force excreted by source and the weight of the object.

This can be proven if canon is shooted towards water, rubber ball will travel further than steel because of the weight of the object.

I had reasoned that the flexibility of the rubber ball would absorb more of the ballistic force than the rigid steel, and thus would travel less far. Of course, at 45°, they would each travel as far as 50 m/s could launch them.

Iron ball will have more momentum so it will go a bit further

Many of the solutions are irrelevant because one of the given conditions is that the cannon fires at 50 m/s, therefore the power/work/force are adjustable for mass/density of projectiles. Since both objects are spheres and of the same size, air friction shouldn't affect them in any different way, at least at those speeds. At higher speeds, the effect of skin friction becomes more noticeable. The atomic surface of rubber is more prone to exchanging momentum with air molecules when compared to the smooth surface of a polished steel ball. The larger the projectile, the more measurable a difference in range.

My initial thought was that the rubber ball has less density therefore more of the cannon's work would go into internal energy rather than kinetic energy, therefore it would leave with less speed, however the initial speed is fixed. Also, yes the steel ball has more kinetic energy due to a higher mass, but that does not give it more range; projectile motion does not depend on mass. The air friction, however, does depend on those masses.

Let the density of steel ball be $\alpha$ and that of rubber ball be $\beta$ .... We know that $\alpha$ > $\beta$ !!!! Let the density of air be $\gamma$ ... Therefore the buoyant force due to air on steel ball and rubber ball is proportional to $\gamma$ !!!!! And frictional force will be proportional to $\alpha$ - $\gamma$ and $\beta$ - $\gamma$ respectively for steel and rubber ball [see I have arrived at this by seeing frictional force as viscous force ] let V be the volume of both the balls then mass of Steel ball will be $\alpha$ V and mass of rubber ball will be $\beta$ V and retardation on steel ball will be proportional to [ $\alpha$ - $\gamma$ ] / $\alpha$ V and retardation on rubber ball will be proportional to [ $\beta$ - $\gamma$ ] / $\beta$ V by seeing the expressions one may mistakingly predict that retardation of Steel ball is more therefore Steel ball goes to a lesser distance but actually this viscous force decreases the maximum height of a projectile but increases the time of flight !!!! [Time of flight for steel ball will be more increased]For horizontal the frictional force acting on both of them will be same therefore less retardation of heavier Steel ball so our both results favours STELLA and STELLA wins !!!!!

Here is the catch. They are of same size (i.e. volume). Since steel has higher density over rubber it will have more mass which means initial momentum of steel ball is higher. Both balls are same size, hence we can assume the drag on both balls are same (air resistance). Therefore as steel ball has higher momentum it will travel further.

At first, i thought it will be a tie because it has to do with the shape of the ball and how air dinamic it is. It also has to do with the force the balls have. Since the steel ball has more mass, it has a lot more kinetic energy ( m*v^2/2) and thus travels further.

Steel Ball is heavier so when launched it will have greater momentum than the rubber ball. The friction and initial velocity will be approximately the same so the steel ball having greater momentum will go farther

At same speed moment of inertia of steel ball is larger than rubber ball.

Presuming the steel ball is heavier than the rubber ball, the fact that they've both been accelerated to the same velocity suggests that more force must have been applied to the steel ball to get it up to that velocity. Where and when it lands would then depend on the momentum, which common sense suggests would be higher in the steel ball, thus greater distance reached.

Even though the balls are same size, there's no assumption that the balls are completely solid. If the middle of the steel ball is hollow, the Steel ball can weight less than the Rubber ball and therefore Stella can loose!

While the math answers are of course true, the situation is kind of overlooking the fact that you are shooting a rubber ball out of a cannon. Is it unreasonable to consider the rubber ball would be damaged by the blast and would contribute to a lack of flight? Maybe the picture is adding to my assumption.

The iron ball has more mass so it therefore has greater inertia: and will travel farther.Gravity doesn't matter since both balls will still fall at the same rate;Unless of course there is air resistance or the rubber ball bounces.

The diameter of both projectiles is equal, the exit velocity has been equalized, obviously more energy given to Stellas gun to produce the equalized exit velocity as rubber is accelerated easier than heavy metal...aerodynamic drag would be equal due to projectile congruity... so the extra energy provided to accelerate Stellas projectile to match the rubber counterpart upon muzzle exit will carry the projectile farther since there are no other appreciable differences in flight dynamics between the two projectiles. That extra energy put into the metal ball to equalize muzzle exit velocity will have to go somewhere... and that being distance traveled. If distance were limited or equalized by say -a wall placed at equal range to both guns, then the extra energy afforded to Stella would be dissipated as impact force.

More projectiles are made of iron than out of rubber. If the projectile were able to cause more turbulence, it would lose horizontal velocity faster and therefore gravity (in vertical downward direction) would win?

Distance= mass x acceleration. The steel ball has more mass, so even though it takes more force to get it going, it will take more force to stop it.