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?
Another ball lies on the street, 9 m out from the base of the same 11 m balcony. Nobody watched the launch. How fast did this ball leave the railing? The two measurements are enough to say.
Two things are measured: the launch height and the landing distance. Each one connects to the flight in a way you have already used. The height gives the flight time, and the range is the horizontal speed multiplied by that time.
Run the two steps in order. First, the height gives the flight time:
t = √(2Δx ÷ g) = √(2 × 11 ÷ 9.8) ≈ 1.5 s
Then the range equation, rearranged, gives the launch speed:
v_x = range ÷ t = 9 ÷ 1.5 = 6 m/s
A ball rolls off a roof 19.6 m above flat ground and lands 15 m from the building's base. Calculate the ball's time of flight.
Write down the values in the question:
Δx = 19.6 m
range = 15 m
t = ?
Write down the equation:
t = √(2Δx ÷ g)
Substitute in the values:
t = √(2 × 19.6 ÷ 9.8) = √4
Simplify:
t = 2.0 s
The same ball: a 19.6 m roof, landing 15 m out, a 2.0 s flight. Calculate its launch speed.
Write down the values in the question:
range = 15 m
t = 2.0 s
v_x = ?
Write down the equation:
v_x = range ÷ t
Substitute in the values:
v_x = 15 ÷ 2.0
Simplify:
v_x = 7.5 m/s
A ball rolls off a parking-garage roof 45 m above the street and lands 24 m out from the building's base. Enter its time of flight in s, to one decimal place.
The same measurements: a ball leaves a parking-garage roof 45 m up and lands 24 m out. Enter its launch speed in m/s, to one decimal place.
A stone is thrown horizontally from a cliff edge 30 m above the sand and lands 30 m out from the cliff's base. Enter its launch speed in m/s, to one decimal place.
A water balloon is launched horizontally from a 50 m tower and bursts on the ground 40 m from the tower's base. Enter its launch speed in m/s, to one decimal place.
A tennis ball rolls off a cliff path 15 m above the sea and splashes 8 m out from the cliff's base. Enter its launch speed in m/s, to one decimal place.
A ball is thrown horizontally from a canyon rim 80 m above the canyon floor and lands 65 m out. Enter its launch speed in m/s, to one decimal place.