I needed some help here with the launching an object off a roofproblem. You are

Question

I needed some help here with the launching an object off a roofproblem. You are on a roof that is 15 meters high and you are launchingballoons off at an angle of 30 degrees above the horizon with aspeed of 20 meters/second. A) What are the horizontal and vertical components of thevelocity of the 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 the horizontal range of the balloons?
You are on a roof that is 15 meters high and you are launchingballoons off at an angle of 30 degrees above the horizon with aspeed of 20 meters/second. A) What are the horizontal and vertical components of thevelocity of the 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 the horizontal range of the balloons?

Explanation / Answer

height of the roof, h = 15 m initial velocity, U = 20 m/s angle of projection, = 30o (a) horizontal component of initial velocity, Ux = U cos = 20 * cos 30o = 17.32 m/s vertical component of initial velocity, Uy = U sin = 20* sin 30 o = 10 m/s (b) maximum height above the ground , H = h + [ ( Uy )2 / 2g ] = 15 + [ 17.322 / ( 2 * 9.8 ) ]= 30.31 m (c) S = Ut + ( 1/2) a t 2 - h = ( Uy ) t - ( 1/2 ) g t2 - 15 = 10 t - 4.9 t 2 4.9 t 2 - 10 t - 15 = 0 by solving above equation, t = 3.05 s (d) Horizontal range, R = ( Ux) t = 17.32 * 3.05 = 52.76 m 4.9 t 2 - 10 t - 15 = 0 by solving above equation, t = 3.05 s (d) Horizontal range, R = ( Ux) t = 17.32 * 3.05 = 52.76 m

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