A marble leaves a tabletop moving horizontally. Halfway down, how does its horizontal velocity compare with its launch value?
A ball leaves a thrower's hand at 20 m/s, 30° above the horizontal, arcs over the field, and comes back down to the height it started from. The launch is easy to describe. What does the landing look like?
Both pieces of the answer are already yours: the horizontal component never changes in flight, and you have seen the up-and-down symmetry of free fall. Together they write the landing for you.
The ball leaves at 20 m/s, 30° above the horizontal, and returns to its launch height. Air resistance is ignored.
Its horizontal velocity component never changes in flight: 17.3 m/s forward at launch, still 17.3 m/s forward at landing.
Its vertical motion is an ideal up-and-down flight, and you have already seen its symmetry: the speed at a given height on the way up equals the speed at that same height on the way down.
The launch height and the landing height are the same height. So the vertical speed at landing equals the vertical speed at launch, 10 m/s, now pointing down.
Same horizontal component, same vertical speed, one direction flipped. So the landing speed is the launch speed, 20 m/s, angled 30° below the horizontal instead of 30° above.
That pattern has a name in this topic: the mirror fact. The landing mirrors the launch.
A softball is thrown at 16 m/s, 37° above the horizontal, and returns to its launch height with air resistance ignored. Describe its landing velocity.
The flight returns to its launch height, so the mirror fact applies.
The landing speed equals the launch speed: 16 m/s.
The landing angle below the horizontal equals the launch angle above it: 37°.
So the softball lands at 16 m/s, angled 37° below the horizontal.
A baseball thrown at 18 m/s returns to its launch height, air resistance ignored. How does its landing speed compare with 18 m/s?
A kickball returns to the height it was kicked from, air resistance ignored. Just before landing, where does its velocity point?
The mirror needs the matched heights. A flight that ends above or below its launch height lands at a different speed, and the mirror fact does not apply.
A ball is thrown upward at an angle from the ground and lands on a shelf above its launch height, air resistance ignored. Does it land at its launch speed?
The mirror fact holds between matched heights only.
This flight ends above its launch height, so the heights are not matched.
The ball lands before it can fall back to launch height, so it lands moving more slowly than it was launched.
No. Landing above the launch height, it lands more slowly than it was launched.
Joel throws a tennis ball upward at an angle, and it comes back down to the height of his hand. Air resistance is ignored. Joel says the ball lands moving at the same speed it had when it left his hand. Is Joel correct?
A lacrosse ball leaves at 33° above the horizontal and returns to its launch height, air resistance ignored. At what angle does it land?
A water balloon is launched at 22 m/s, 41° above the horizontal, and returns to its launch height, air resistance ignored. Which is its landing velocity?
Three identical balls are thrown at 15 m/s, air resistance ignored. One lands back at its launch height, one lands on a roof above its launch height, one lands in a hollow below its launch height. Which ball lands moving at 15 m/s?