So if the initial velocity is +5, then the final velocity has to be -5. However, we should easily see that the projectile was at first going up, but then it finishes by going down, thus we have to write the y component of the final velocity with the opposite sign of the y component of the initial velocity. And since the starting and ending points have the same elevation, we can then assume that the projectile has equal speed at those two points. We assume this to be true since we are also assuming that there is no air resistance. So we choose the final velocity to be just before it hits the ground.Īnd what is the final velocity before it hits the ground? Well, the projectile does not lose any energy while from the time right after it is launched to the time just before it lands. Fortunately, this problem can be solved just with the motion of the projectile before it hits the ground, so we don't need to concern ourselves with anything after that. Then only after it hits the ground will it have zero velocity, but hitting the ground will introduce another force to this system, and we would need to use more equations to describe its motion. Just before it hits the ground, the projectile has some downward speed. So we should only apply them to the motion of the projectile right after it is thrown and right before it hits the ground. This means that the only force acting on it is the force of gravity. The equations that we are using to solve this problem only apply when the projectile is in free fall.
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