Wildlife biologists fire 22g rubber bullets to stop a rhinoceros charging at 0.84 m/s. The bullets strike the rhino and drop vertically to the ground. The biologists' gun fires 15 bullets each second, at 72 m/s, and it takes 36 s to stop the rhino. What impulse does each bullet deliver? as well as What's the rhino's mass? Neglect forces between rhino and ground.
impulse = change in momentum = .022*72 for each bullet
total change in bullet momentum + total change in rhino momentum = 0
so
number of bullets*.022*72 = m * .84
For part b, divide the speed of the rhino by the time it takes to stop it which would give you the acceleration.
That trajectory flatness need to be accounted for. That is already forgo the smaller variability already which is of limited consequence but just for the information
Must not most in previous phrase
Well, well, well, we have some wild wildlife action going on here! Let's break it down.
We know that each bullet has a mass of 22g, which is the same as 0.022kg. The gun fires 15 bullets per second, so each second it delivers an impulse of:
Impulse = (mass of bullet) x (velocity) = 0.022kg x 72m/s = 1.584 kg·m/s
Impressive, right? Each bullet delivers an impulse of 1.584 kg·m/s.
Now, let's find out the rhino's mass. To stop a charging rhino, it takes 36 seconds. Since we know the impulse and duration of the interaction, we can use the impulse-momentum equation:
Impulse = (mass of rhino) x (change in velocity)
The change in velocity is from the initial velocity of 0.84 m/s to 0 m/s when the rhino stops.
Impulse = (mass of rhino) x (change in velocity)
1.584 kg·m/s = (mass of rhino) x (-0.84 m/s)
To get the mass of the rhino, we rearrange the equation:
(mass of rhino) = Impulse / (change in velocity)
(mass of rhino) = 1.584 kg·m/s / (-0.84 m/s)
(mass of rhino) ≈ -1.886 kg
Wait a second! Negative mass? That doesn't make any sense! It seems like we made a mistake somewhere. Let's double-check our calculations.
Oh, silly me! I apologize for the confusion. It seems I've made a bit of a calculation blunder. The mass of the rhino can't be negative, of course. So let's fix it.
The equation is correct, but we made a sign error in the calculation. The rhino's mass is:
(mass of rhino) = Impulse / (change in velocity)
(mass of rhino) = 1.584 kg·m/s / (0.84 m/s)
(mass of rhino) ≈ 1.886 kg
There you have it! The mighty rhino has a mass of approximately 1.886 kg. Impressive, considering the rubber bullets had to bring it to a halt!
To find the impulse delivered by each bullet, we can use the formula:
Impulse = Change in momentum
The momentum of an object is given by the equation:
Momentum = mass × velocity
Let's calculate the impulse delivered by each bullet:
Given:
Mass of each bullet = 22 grams = 0.022 kg
Velocity of each bullet = 72 m/s
Impulse = Change in momentum
The change in momentum is equal to the final momentum minus the initial momentum. Since each bullet comes to a stop after hitting the rhino, the final momentum is zero.
Initial momentum = mass × velocity
Final momentum = 0
Therefore, the impulse delivered by each bullet is:
Impulse = Final momentum - Initial momentum
Impulse = 0 - (mass × velocity)
Impulse = -(0.022 kg × 72 m/s)
Impulse = -1.584 Ns (Newtons-second)
Now, let's find the mass of the rhino using the given information:
Given:
Time taken to stop the rhino = 36 seconds
Velocity of the rhino = 0.84 m/s
Impulse = Change in momentum
Again, the change in momentum is equal to the final momentum minus the initial momentum. Since the rhino comes to a stop, the final momentum is zero.
Initial momentum = mass × velocity
Final momentum = 0
Therefore, the impulse delivered to the rhino is:
Impulse = Final momentum - Initial momentum
Impulse = 0 - (mass × velocity)
Impulse = -(mass × 0.84 m/s)
Impulse = -1.584 Ns (Newtons-second)
But we know that the impulse is also equal to the force multiplied by time:
Impulse = Force × Time
Let's rearrange the equation to solve for force:
Force = Impulse / Time
Substituting the values we have:
-1.584 Ns / 36 s = -0.044 N
Since the force is negative, it implies that the force is acting in the opposite direction of motion. In this case, it represents the force exerted by the rhino.
Now we can calculate the mass of the rhino using Newton's second law:
Force = mass × acceleration
Given:
Force = -0.044 N
Rearranging the equation to solve for mass:
mass = Force / acceleration
Since the rhino comes to a stop, the acceleration is given by:
acceleration = (Change in velocity) / Time
acceleration = (0.84 m/s - 0 m/s) / 36 s
acceleration = 0.84 m/s / 36 s
acceleration = 0.0233 m/s²
Substituting the values we have:
mass = -0.044 N / 0.0233 m/s²
mass ≈ -1.887 kg
The negative sign indicates that the direction of the force and acceleration are opposite to each other.
Therefore, the mass of the rhino is approximately 1.887 kg, and each bullet delivers an impulse of -1.584 Ns (opposite to the motion).
Answer to 1 is it doesn’t matter, to question 2 also it doesn’t matter. You will be dead, 22g rubber bullet is so light won’t even have scratch and bounce off. This question is not responsible, specially for people who don’t know or kids. Anything short of a .450 even a 404 with at least 350 grain at least full metal jacketed with multiple shot just isn’t going to stop it before it crush you. If you miss the brain and just hit body with double barrel 450 I say good luck and may hope you live. Recommend 500+ gr for shotgun and at least a 400 gr 404. Usually I would recommend more the .416 to be safe. Personally I would say have a 458 Lott if you want bullet rifle. Lesser 458win work too though prefer the first. 460 Wby would do great work too.
Could also with extreme luck have a pet leopard to protect you as I have heard a story of it when younger of a female researcher/ranger. It was a rhino charge though and hippo is a case above rhino power, still could work.
Even within the rubber bullet context, it is a flawed question, bullet bc, velocity, case capacity and ftb of energy most be accounted not to forget