C O N C E P T U A L C H E C K P O I N T
C O M PA R E L A N D I N G S P E E D S
You and a friend stand on a snow-covered roof. You both throw snowballs with the same initial speed, but in different directions. You throw your snowball downward, at 40° below the horizontal; your friend throws her snowball upward, at 40° above the horizontal. When the snowballs land on the ground, is the speed of your snowball (a) greater than, (b) less than, or (c) the same as
the speed of your friend’s snowball?
R E A S O N I N G A N D D I S C U S S I O N
One consequence of symmetry in projectile motion is that when your friend’s snowball returns to the level of the throw, its speed will be the same as the initial speed. In addition, it will be moving downward, at 40° below the horizontal. From that point on its motion is the same as that of your snowball; thus it lands with the same speed.
What if you throw your snowball horizontally? Or suppose you throw it straight down?
In either case, the final speed is unchanged! In fact, for a given initial speed, the speed on landing simply doesn’t depend on the direction in which you throw the ball.
A N S W E R
(c) The snowballs have the same speed
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