Why does a ball rolling off a level shelf start its flight with zero vertical velocity?
A ball rolls off a balcony railing 11 m above the street. How long is the ball in the air? The question never states the launch speed, and the answer will not need it.
The flight ends when the ball has fallen 11 m, and only the vertical motion covers that 11 m. A horizontal launch starts with zero vertical velocity, so the ball's vertical motion is a drop from rest.
A drop from rest obeys the free-fall equation you have used on dropped objects: Δx = ½gt². Here Δx is the distance fallen in m, g is the free-fall acceleration, 9.8 m/s², and t is the time of flight in s.
The flight time is the time the drop takes. To find it, make t the subject: t = √(2Δx ÷ g).
For the balcony ball:
t = √(2 × 11 ÷ 9.8) ≈ 1.5 s
You have already seen the rule this equation puts numbers on: the launch height sets the flight time, and the launch speed does not change it. From 11 m up, every horizontal launch speed gives the same flight time of about 1.5 s.
A ball rolls off a flat roof 20 m above the ground. Calculate its time of flight.
Write down the values in the question:
Δx = 20 m
g = 9.8 m/s²
t = ?
Write down the equation:
Δx = ½gt²
Make t the subject:
t = √(2Δx ÷ g)
Substitute in the values:
t = √(2 × 20 ÷ 9.8) = √4.08
Simplify:
t = 2.0 s
A marble leaves a tabletop 0.8 m above the floor at 2.5 m/s. Which given value decides the marble's time of flight?
A stone is flicked horizontally at 8 m/s from a cliff edge 45 m above the sea. Calculate its time of flight.
Write down the values in the question:
Δx = 45 m
g = 9.8 m/s²
t = ?
The 8 m/s launch speed is horizontal, so it plays no part in the fall.
Write down the equation:
t = √(2Δx ÷ g)
Substitute in the values:
t = √(2 × 45 ÷ 9.8) = √9.18
Simplify:
t = 3.0 s
A ball rolls off a shelf 2.2 m above the floor. Enter its time of flight in s, to one decimal place.
A ball rolls off a platform 7.2 m above the ground at 5 m/s. Enter its time of flight in s, to one decimal place.
A marble rolls off a workbench 0.9 m above the floor. Enter its time of flight in s, to one decimal place.
A skateboard rolls horizontally off a loading dock at 4.5 m/s. The dock stands 1.1 m above the lot. Enter the skateboard's time of flight in s, to one decimal place.
A ball is thrown horizontally from a bridge deck 60 m above a river. Enter its time of flight in s, to one decimal place.