So our velocity is going toĭecrease at a constant rate. So the y component, it starts positive, so it's like that, but remember our acceleration Magnitude of its y component, and then this would be the This vector right over here, the head of it, and go to the left, and so that would be the Initial velocity vector that has this velocity at an angle and break it up into Velocity in the y direction for this first scenario? Well we could take our The acceleration due to gravity once the ball is actually With which you throw it, that doesn't somehow affect Here is going to be true for all three of these scenarios because the direction So it's just going to be, it's just going to stay right at zero and it's not going to change. To be any acceleration or deceleration in the x direction. Now what about in the x direction? Well if we assume no air resistance, then there's not going Once the projectile is let loose, that's the way it's And if the magnitude of the acceleration due to gravity is g, we could call this negative g to show that it is a downward acceleration. We're going to assumeĬonstant acceleration. Gravity will be downwards, and it's going to be constant. In the vertical direction? Well the acceleration due to Type of a laboratory vacuum and this person had maybeĪn astronaut suit on even though they're on Earth. We're assuming we're onĮarth and we're going to ignore air resistance. So let's first think about acceleration in the vertical dimension, acceleration in the y direction. Or even take out some paper and try to solve itīefore I work through it. So I encourage you to pause this video and think about it on your own Time graphs look like in both the y and the x directions. These initial velocity vectors, what would the acceleration versus time, the velocity versus time, and the position versus To do in this video is think about for each of And here they're throwing the projectile at an angle downwards. They're not throwing it up orĭown but just straight out. The edge of a cliff on Earth, and in this first scenario, they are launching a Hence, Sal plots blue graph's x initial velocity(initial velocity along x-axis or horizontal axis) a little bit more than the red graph's x initial velocity(initial velocity along x-axis or horizontal axis).Įach of these pictures we have a different scenario. It'll be the one for which cos Ө will be moreįor red, cosӨ= cos (some angle>0)= some value,say x0)=x initial velocity of red ball Now, let's see whose initial velocity will be more. Now, assuming that the two balls are projected with same |initial velocity| (say u), then the initial velocity will only depend on cosӨ in initial velocity = u cosӨ, because u is same for both. In this case/graph, we are talking about velocity along x- axis(Horizontal direction)įor blue ball and for red ball Ө(angle with which the ball is projected) is different(it is 0 degrees for blue, and some angle more than 0 for red) This means that cos(angle, red scenario) < cos(angle, yellow scenario)! Hence, the horizontal component in the third (yellow) scenario is higher in value than the horizontal component in the first (red) scenario. It actually can be seen - velocity vector is completely horizontal.Ģ) in yellow scenario, the angle is smaller than the angle in the first (red) scenario. This means that the horizontal component is equal to actual velocity vector. In this case, this assumption (identical magnitude of velocity vector) is correct and is the one that Sal makes, too).ġ) in blue scenario, the angle is zero hence, cosine=1. So from our derived equation (horizontal component = cosine * velocity vector) we get that the higher the value of cosine, the higher the value of horizontal component ( important note: this works provided that velocity vector has the same magnitude. If we work with angles which are less than 90 degrees, then we can infer from unit circle that the smaller the angle, the higher the value of its cosine. Now we get back to our observations about the magnitudes of the angles. Horizontal component = cosine * velocity vector After manipulating it, we get something that explains everything! We do this by using cosine function: cosine = horizontal component / velocity vector. If above described makes sense, now we turn to finding velocity component. All thanks to the angle and trigonometry magic.Īfter looking at the angle between actual velocity vector and the horizontal component of this velocity vector, we can state that:ġ) in the second (blue) scenario this angle is zero Ģ) in the third (yellow) scenario this angle is smaller than in the first scenario.
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