What minimum horizontal velocity u can a boy throw a rock at A and have it just clear the obstruction?

A student on the ground fires a pebble from a catapult with a velocity of 30 m/s at an angle of 30° above the horizontal.  If the pebble’s flight is interrupted by a vertical wall 12 m away from the student, at what height above the ground does the pebble hit the wall?

Sweden and Norway are at war over who makes the best pickled herring. You are in charge of a Swedish artillery unit that is trying to shoot at some Norwegians located 1000 meters away at the same height as you are. If we neglect the friction of the air, the cannon ball follows a parabolic trajectory; as you certainly recall from prior courses, a cannon ball travels a distance L = V²sin(2a) 9 where V is the initial velocity, a is the angle of the cannon barrel, and g = 9.8 m/s² is the gravitational acceleration. You realize that you only have two options for how to shoot. Option (I) is to use 1 bag of gun powder, which produces an initial velocity of exactly V₁ = 105 m/s, and to try to set the angle to aI,nominal = 39 degree. Option (II) is to use 2 bags of gun powder, which produces exactly VII = 137 m/s, and to try to set the angle to aII,nominal = 15 degree. If you set the angles exactly to the nominal ones, compute the traveling distances. L₁ = LII = The problem is that the cannon…

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