Your forehead can withstand a force of about 6.0 kN before fracturing, while your cheekbone can withstand only about 1.3 kN. Suppose a 140 g baseball traveling at 30 m/s strikes your head and stops in 1.5 ms. a.What is the magnitude of the force that stops the baseball?

Video transcript

Hi, everyone in this practice problem. We're being asked to calculate the strength of the force applied by the goalkeeper to actually stop the ball. We will have a professional football player kicking a 450 grand ball at a speed of 90 km an hour. The goalkeeper stops the ball with his hands and brings it to rest in 0.5 seconds. We're being asked to calculate the strength of the force applied by the goalkeeper in order to actually stop the ball. And the options given are a 22.5 Newton B Newton C 100 and 11 Newton and D 400 Newton. So in order for us to calculate this problem, uh first, what we wanna do is to calculate the average acceleration that encounters the ball in order for it to decrease from the speed of 90 kilometers an hour to rest. So the speed given or the V X or I'm just gonna say V I is going to be kilometers an hour and we want to convert this 90 kilometers an hour, two m per second so that it's easier for us to use in the next calculation. So we're gonna multiply this by 1000 m per one kilometer and multiply this by one hour per 3600 seconds. And that will give us 25 m per seconds, which is going to be our initial velocity. Our final velocity V F is going to be zero m per second, which is at rest or at stop. And to find the deceleration of the ball, we will apply the following kinematic equation. So the kinematic equation that we're going to use is going to be V F equals a of the ball multiplied by the time plus V I. And we can rearrange this so that we get uh an equation for the acceleration of the ball, which in this case is then going to be V F minus V I divided by C. So we know all this information V F is going to be zero m per second. V I is going to be 25 m per second. And the time that it takes for it to go from 90 kilometers an hour to stop is 0.5 seconds. So therefore the acceleration or in this case deceleration is going to be negative 50 m per second squared just like so awesome. So now that we found our deceleration, we can actually calculate the strength of the force that stopped the ball by applying Newton 2nd Law. So applying Newton 2nd Law, we can then calculate our force. So according to Newton's second law, F net will equals to the mass of our system which is the ball multiplied by the acceleration of the ball or in this case, deceleration. So The mass of the ball is given to be 450 g, which is 450 times 10 to the power of - kg. And uh deceleration is minus 50 m per second squared because we are looking at the net force. So we are only looking at the magnitude. So I'm just going to put an absolute value inside our deceleration or acceleration. And therefore F net will then be Equals to 22.5 Newton. So 22.5 Newton is going to be the strength of the force applied by the goalkeeper in order to actually stop the ball. So that will correspond to option a in our answer choices. So answer a is going to be the answer to this particular practice problem with the strength of the force being 22.5 Newton. So that'll be all for this particular practice problem. If you guys still have any sort of confusion, please make sure to check out our other lesson videos on similar topics and they'll be all. Thank you.