If an object travels one-half its total path in the last second of its fall from rest, find (a) the time and (b) the height of its fall

If an object travels one-half its total path in the last second of its fall from rest, find (a) the time and (b) the height of its fall. Explain the physically unacceptable solution of the quadratic time equation.

[ Ans: (a) 3.4 sec  (b) 57m ]

A ball is falling from the top of a cliff of height h with an initial speed V. Another ball is simultaneously projected vertically up with the same speed. When do they meet

A ball is falling from the top of a cliff of height h with an initial speed V. Another ball is simultaneously projected vertically up with the same speed. When do they meet ?

[ Ans: h/2V ]

A rocket is fired vertically up from the ground with a resultant vertical acceleration of 10 m/s2 . The fuel is finished in 1 minute and it continues to move up

A rocket is fired vertically up from the ground with a resultant vertical acceleration of 10 m/s2 . The fuel is finished in 1 minute and it continues to move up
(a) what is the maximum height reached ?
(b) After how much time from then will the maximum height be reached ? (Take g = 10 m/s2 )

[ Ans: (a) 36 km     (b) 1 minute ]

A football player kicks the football so that it will have a ” hang time ” (time of flight) of 5s and lands 50 m away. If the ball leaves the player’s foot 1.5m above the ground, what is its initial velocity (magnitude and direction)? (g = 10 m/sec2 )

A football player kicks the football so that it will have a ” hang time ” (time of flight) of 5s and lands 50 m away. If the ball leaves the player’s foot 1.5m above the ground, what is its initial velocity (magnitude and direction)? (g = 10 m/sec2 )

[ Ans: 26.64 m/s, 67.96° ]

A bomb is released from an aeroplane flying with a horizontal velocity of magnitude 100 m/sec at an altitude of 1 km. What is the displacement during the time of its flight

A bomb is released from an aeroplane flying with a horizontal velocity of magnitude 100 m/sec at an altitude of 1 km. What is the displacement during the time of its flight ?

[ Ans: 1732 m ,  tan-1(0.707) ]