Question

Consider two cases, in case (a) a ball that has been thrown straight upward from the edge of a cliff. The initial speed of the ball is $20 m s^{- 1}$ . It goes up and then falls back down, eventually hitting the ground beneath the cliff. In case (b) the ball has been thrown straight downward at the same initial speed. In the absence of air resistance, would the ball in case (b) strike the ground with (i) smaller speed than in case (a), (ii) same speed as in case (a), or (iii) greater speed than the ball in case (a)?

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Accepted Answer

We know in the absence of air resistance and the motion is that of free-fall type we can analyse the motion by symmetry consideration. In the figure, we can observe that the ball after it has been thrown upward has fallen back down to its starting point. Symmetry suggests that the speed in figure is the same as in ease ( $a$ ) - lamely, $20 m s^{- 1}$ as is also the case when the ball has been actually thrown downward. Consequently, whether the ball is thrown as in case ( $a$ ) or ( $b$ ), it begins to move downward from the cliff edge at a speed of $20 m s^{- 1}$ . In either case, there is the same acceleration due to gravity and the same displacement from the cliff edge to the ground below. Under these conditions, the ball reaches the ground with the same speed in both cases ( $a$ ) and ( $b$ ).

B M Sharma Solutions for Chapter: Kinematics I, Exercise 25: ILLUSTRATION 4.23

B M Sharma Physics Solutions for Exercise - B M Sharma Solutions for Chapter: Kinematics I, Exercise 25: ILLUSTRATION 4.23

Questions from B M Sharma Solutions for Chapter: Kinematics I, Exercise 25: ILLUSTRATION 4.23 with Hints & Solutions

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