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A cannon ball is fired from top of a building at an angle 30 degree above horizontal...

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user8235304 | Student, Grade 11 | Valedictorian

Posted June 15, 2013 at 4:26 AM via web

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A cannon ball is fired from top of a building at an angle 30 degree above horizontal with speed 60 m/s.Another cannon ball is projected from the same spot with same speed at an angle 30 degree below horizontal.The first ball hits the ground at a distance double of that of second one.Find the height of the tower.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 16, 2013 at 3:17 AM (Answer #2)

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A cannon ball fired from top of a building at an angle 30 degree above horizontal with speed 60 m/s travels twice the horizontal distance as a cannonball projected from the same spot with same speed at an angle 30 degree below horizontal.

Let the time taken by the first cannonball to strike the ground be t. If the height of the building is H,

H = 60*sin 30*t - (1/2)*9.8*t^2

The horizontal distance traveled by the cannon ball is D = 60*cos 30*t.

Let the time taken by the second cannon ball to strike the ground be t'. As the direction of acceleration is downwards and the cannonball is also projected at 30 degrees below the horizontal H = 60*sin 30*t' + (1/2)*9.8*t'^2

The horizontal distance traveled is D' = 60*cos -30*t'

As D = 2D'

=> 60*cos 30*t = 2*60*cos -30*t'

=> t = 2*t'

60*sin 30*t - (1/2)*9.8*t^2 = 60*sin 30*t' + (1/2)*9.8*t'^2

=> 60*sin 30*2*t' - (1/2)*9.8*4*t'^2 = 60*sin 30*t' + (1/2)*9.8*t'^2

=> 60*sin 30*t' = (5/2)*9.8*t'^2

=> 60 = (5/2)*9.8*t'

=> t' = 60/49

H = 60*sin 30*t' + (1/2)*9.8*t'^2

H = 2160/49 m

The height of the building is 2160/49 m

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 15, 2013 at 12:08 PM (Reply #1)

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The formula for the vertical distance traveled by the canonballs does not have the term cos 30, rather it is H = 60*sin 30*t - (1/2)*9.8*t^2 for the first cannon ball and H = 60*sin -30*t - (1/2)*9.8*t^2 for the second.

The height that has been determined is incorrect.

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