Mr. Smith is on top of a building launching waterballoons. Let\'s assume he is 1

Question

Mr. Smith is on top of a building launching waterballoons. Let's assume he is 15 meters above the ground andhe is launching them at an angle of 30 degrees above the horizonwith a speed of 20 meters/second. A) What are the horizontal and vertical components of thevelocity of teh balloons at the moment of launch? B) What will be the maximum height above the ground theballoons will reach? C) How long will the balloons be in the air? D) What will be teh horizontal range of the balloons? Mr. Smith is on top of a building launching waterballoons. Let's assume he is 15 meters above the ground andhe is launching them at an angle of 30 degrees above the horizonwith a speed of 20 meters/second. A) What are the horizontal and vertical components of thevelocity of teh balloons at the moment of launch? B) What will be the maximum height above the ground theballoons will reach? C) How long will the balloons be in the air? D) What will be teh horizontal range of the balloons?

Explanation / Answer

Initial height h = 15 m angle = 30 degrees velocity v = 20 m / s (A). the horizontal components of the velocity of tehballoons at the moment of launch = v cos 30 = 17.32 m / s The vertical component of velocoty = v sin 30 = 10 m /s B) the maximum height above the ground the balloons will reach= h + ( v sin 30 ) ^ 2 / 2g                                                                                                = 15 + ( 100 / 19.6 )                                                                                                = 20.1 m C) time in air t = ? In vertical direction initial speed u= v sin 30 = 10 m /s accleration a = -g = -9.8 m / s ^ 2 displacement h = 15 m from the relation h = ut - ( 1/ 2) g t ^ 2                     -15= 10 t - 4.9 t ^ 2 4.9 t ^ 2 -10t -15 = 0 t = { 10 ± [ -10^2 -( 4 * 4.9 * -15 ) ] } /2( 4.9 ) = { 10 ± [ 100+ 294 ] } / 9.8 = { 10 ± 19.84 } / 9.8 = 3.045 s     Since time ispositve (D). horizontal range = v cos 30 * t                                 = 52.75 m      

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