A boy throws a ball with initila velocity u at an angle of porjection theta from a tower of height H. Neglecting air resistance, find (a) how high above the building the ball rise, and (b) its speed just before it hits the ground.

A boy throws a ball with initila velocity u at an angle of porjection

1.	A boy throws a ball with initila velocity u at an angle of porjection theta from a tower of height H. Neglecting air resistance, find (a) how high above the building the ball rise, and (b) its speed just before it hits the ground.
Answer» Solution :(a) Only gravitational force acts on the ball, which is conservative, therefore we can apply CONSERVATION of energy i.e., U = 0. At the topmost point in the path, the ball is moiving horizonrally with VELOCITY `ucos theta`. Initial total mechanical energy, `E_(i) = 0 + (1)/(2) m u^(2)` Total mechanical energy at thetopmost point : `E_(r) = (1)/(2) m u^(2) cos^(2)theta + mgh` From conservation of energy, we have `E_(i) = E_(r)` (a) `(1)/(2) m u^(2) = (1)/(2) MU^(2) cos^(2) theta + mgh` or `h = (u^(2) - u^(2) cos^(2) thea)/(2g)` (b) If v is the SPEED of the ball at the ground, `E_(f) = (1)/(2) mv^(2) - mgh` From conservation of energy, wehave `E_(i) = E_(f) RARR(1)/(2)m u^(2) = (1)/(2)mv^(2)-mgH.v=sqrt(u^(2)2gH)`