a ball is thrown from the ground at an angle of 30 degrees above the horizontal

Question

a ball is thrown from the ground at an angle of 30 degrees above the horizontal towards a building that is 3.5 m high. When the ball is released, it is traveling at a soeed of 45 m/s How long after being released does the ball hit the top of the building?

Explanation / Answer

initial velocity in vertical direction = 45*sin(30) = 22.5 m/s it is decelerated by g therefore h = 22.5*t-0.5*9.8*t^2 =>4.9*t^2-22.5t+3.5 = 0 on solving we get t = 0.16 s , t = 4.43 s time of flight = 2*45*sin(30)/9.8 = 4.59 sec therefore time taken to reach max. height would be 2.29 sec depending on location of building along X direction,it may hit either after 0.16 s or 4.43 s

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