(II) An 85-g arrow is fired from a bow whose string exerts an ...

Question

(II) An 85-g arrow is fired from a bow whose string exerts an average force of 105 N on the arrow over a distance of 75 cm. What is the speed of the arrow as it leaves the bow?

Accepted Answer

Hey, everyone in this problem, an 86 g ball is catapulted from a slingshot during its release, the slingshots elastic band exerts an average force of 106 newtons on the ball over a distance of 0.76 m. And we're asked to determine the ball's exit speed. We have four answer choices all in meters per second. Option. A 23 option B 33 option C 40 option D 43. So let's start with the information we've been given in the problem. So we've been told that our ball has a mass M of 86 g and we can write this as 0.086 kg. OK. Converting to our standard units, we have AAA force, an average force. We'll call that a average of 106 newtons and the force is applied over a distance D of 0.76 m. OK? So that's everything we've been told in the problem. And we want to find the ball's exit speed. So we have some information about force and distance. We wanna think about how we can relate this to speed. We recall that the work done W is equal to the change in kinetic energy delta K. And we know we're talking about kinetic energy that those equations are gonna contain the speed. OK. So we have a way to get the speed into this equation already. But what about the work? And while we recall the work is just gonna be our average force a average multiplied by the distance that force is applied to those two values We were given in the problem. We have F average multiplied by D is gonna be the change in kinetic energy. So our final kinetic energy KF minus our initial kinetic energy came up. They recall that kinetic energy is equal to one half mass multiplied by speed squared. So we have F average multiplied by D is equal to one half MVF squared minus one half MV not squared. OK. So now we have an equation where we have F average and D those values we were given, we have the mass which we know we have VF that final speed or the exit speed that we're looking for. So the only other unknown in our equation is the, not the initial speed and the initial speed in this case is going to be zero. OK. That suns Shotts gonna pull back and right before it launches that ball, it's gonna come to rest. So that ball is gonna start from rest before the force is applied and it gets catapulted. OK. So V not, is going to be zero. And we're just left with f average multiplied by D is equal to one half MVF squared. Let's go ahead and substitute in our values and solve. So we have 106 noons multiplied by 0.76 m is equal to one half multiplied by 0.086 kg multiplied by VF squared. And we can simplify on both sides. We get 80.56 Newton meters is equal to 0.0 or 3 kg, multiplied by VF squared, dividing both sides by 0.043 kg. We get that VF squared is equal to 80.56 Newton meters divided by 0.043 kg. Now, if we think about our units here and Newton recall is equivalent to a kilogram meter per second squared. So in the numerator, if we have Newton multiplied by meter, we have kilogram meter squared per second squared. We divide that by kilograms. We're left with meters squared per second squared. And then in the last step, when we take the square root, we're just gonna end up with meters per second, which is the unit we want for speed. And when we take the square root, we get that this final speed or the exit speed is gonna be approximately 43.28 38 meters per second. Ok. So that is the exit speed of the ball from the slingshot if we go up and compare this to the answer choices we were given, we're going round to the nearest meter per second and we can see that the correct answer is going to be option D 43 m per second. Thanks everyone for watching. I hope this video helped see you in the next one.

Struggling with Physics?

(II) An 85-g arrow is fired from a bow whose string exerts an average force of 105 N on the arrow over a distance of 75 cm. What is the speed of the arrow as it leaves the bow?

Watch next

Net Work & Work-Energy Theorem practice set