You throw a baseball straight upward. The drag force is proportional to υ2. In terms of g, what is the y-component of the ball's acceleration when the ball's speed is half its terminal speed and (a) it is moving up?

Video transcript

Welcome back everybody, We have a tennis ball that is tossed vertically upward. Now as it is traveling upward we're going to have a couple of forces acting on it of course are going to have the force due to gravity but we are also going to have a drag force that is acting in the opposite direction of motion. Now, since both of these forces are pointing downwards we are going to have a total vertical acceleration going downwards and this is what we are tasked with finding when we have a speed, that is half of the terminal velocity of this ball. Now our drag force here is proportional to our terminal velocity squared by some proportionality constant, which I'm just going to call C Right now let's go ahead and look at Newton's second law for this scenario. Newton's second law states that the sum of all forces in a given direction, we're going to look in the Y direction is equal to our mass times are vertical acceleration component, so let's go ahead and plug in our values here. Right. This shows that we have our Drag Force which is negative since 20 downwards minus our force due to gravity equal to our mass times our acceleration component, which is also negative, dividing by negative M on both sides that are a Y. Is equal to our drag force plus our force due to gravity divided by our mass. But what is our drag force? Well, we can use this little sort of cheat code here, right at terminal velocity, we have that our drag force is equal to our force due to gravity, which once again our drag force is proportional to the proportionality constant times our terminal velocity squared, meaning that M. G is equal to that as well. But we are looking or a Y. At this philosophy. So let's plug in this philosophy into this formula. Right here we have that our drag force equal to c. Times half of our terminal velocity squared, which just equals 0.5 I'm c B D squared. But we've established that is equal to MG. So our drag force is just 0.25 times our force due to gravity. Now that we have that, let's plug that into this formula right here are vertical acceleration component is our drag force of 0.25 MG plus MG. Divided by M. Giving us that our vertical acceleration is 1.25 times the acceleration due to gravity corresponding to our final answer choice of the Thank you all so much for watching. Hope this video helped. We will see you all in the next one