← Free fall

Same height, same speed

A juggling club is tossed straight up and later caught at the height it left from. Air resistance is ignored. Compare the time the club spends rising with the time it spends falling.

You've already seen that the rise and the fall of an ideal flight take equal times. The symmetry has a second half. This one is about speeds.

launch height19.6 m/sA ball leaves the launch height at 19.6 m/s, straight up. Air resistance ignored.
launch heightthe topThe rise ends at the top — v = 0 for an instant, the acceleration still 9.8 m/s² downward.The fall retraces the same path.
launch height19.6 m/sBack at the launch height the ball moves at 19.6 m/s again — the launch speed, now directeddownward.
An ideal up-and-down flight is symmetric: the speed at a given height on the way up equals the speed at that same height on the way down.
a height the flight visits twiceup passdown passthe two arrows are the same lengthMark any height the flight visits twice: equal arrow lengths — the up-pass speed equals thedown-pass speed.

The speeds match; the velocities don't — the direction has reversed, so with up positive, +19.6 m/s on the way up returns as −19.6 m/s.

positive direction: uplaunch height+19.6 m/s−19.6 m/sThe speeds match; the velocities do not: with up positive, +19.6 m/s on the way up returnsas −19.6 m/s.

'Ideal' means air resistance is ignored. With air resistance the downward pass is slower, so the rule is stated for ideal flights.

Try it on a fresh case. A ball thrown straight up passes a balcony railing at 6 m/s on the way up, with air resistance ignored. Its speed passing the railing on the way down is 6 m/s: the speed at a given height on the way up equals the speed at that same height on the way down. The velocity has reversed; the ball now moves downward.

A ball is thrown straight up at 14 m/s and later falls back through the height it was released from. Air resistance is ignored. What is its speed at that moment? Enter the speed in m/s.

On its way up, a tossed ball passes the top of a tree at 9 m/s. Air resistance is ignored. What is its speed as it passes the treetop on the way down? Enter the speed in m/s.

A ball thrown straight up passes a window ledge at 12 m/s on the way up. Air resistance is ignored. Taking up as positive, what is its VELOCITY as it passes the ledge on the way down? Enter the value in m/s, including its sign.

Your turn

A ball leaves a thrower's hand moving straight up at 23 m/s and is caught at exactly the height it left from. Air resistance is ignored. What is its speed at the catch? Enter the speed in m/s.

Milo throws a ball straight up and catches it at the height he released it. He claims it comes back moving faster than it left, 'because it has been falling and gaining speed the whole way down.' Air resistance is ignored. Which response is correct?

A dart is tossed straight up and passes a shelf at 7 m/s on the way up. Air resistance is ignored. Which statement describes its motion as it passes the shelf on the way down?