A parachutist falling freely throws a ball horizontally. Describe the path observed by the man on the parachute. Would this answer change if the ball was simply dropped by the man on parachute.

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Solution

in the first case the man throws the object horizontally
here he does not give the ball any vertical velocity.
so the ball initialy had the velocity of the man in the parchute(because the ball was travelling with him before he threw it).As he did not impart any additional velocity in vertical direction,the ball will have the same vertical velocity as the man through out and they will always be on the same height from ground.but he imparted a velocity in the horizontal direction.so for him the ball appear to be moving horizontaly in a straight line.(because although their altitude changes this happens for both of them at the same rate and they always be in the same height)
ONLY IF THE PARACHUTE IS NOT WORKING PROPERLY
IF ITS START WORKING PROPERLY THEN IT WILL SLOW DOWN GOING DOWNWARDS AND THE RELATIVE HEIGHT OF BOTH THE MAN AND BALL MAY CHANGE.SO THEN THE BALL APPEAR TO HIM AS MOVING HORIZONTALY AND VERTICALY THAT WILL GIVE HIM THE SHAPE OF A HALF PARABOLA.
in the next case he just drops the ball then he dont impart any velocity in the horizontal and vertical direction.hence the ball and the man does not have any difference in height and also in the horizontal distance.so for the parachutist the ball appear to be in rest
BUT IF THE PARACHUT START WORKING PROPERLY IT WILL SLOW DOWN BUT THE BALL WONT.SO THEIR ALTITUDE MAY CHANGES BUT NOT THE HORIZONTAL DISTANCE HENCE THE BALL APPEAR TO HIM AS GOING VERTICALY DOWN.THAT IS GOING DOWN IN A STRAIGHT LINE

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