An object with starting velocity v₀ accelerates at a constant rate a for a time t. Which equation gives its displacement?
A wrench slips from a scaffold platform 78.4 m above the ground. How long until it hits? The tool is the displacement equation you've already seen, Δx = v₀t + ½at², specialized to a drop.
A dropped object starts from rest, so v₀ = 0 and the v₀t term contributes nothing: the equation becomes Δx = ½at².
Take down as the positive direction: the height fallen is the displacement Δx, and a = +9.8 m/s².
A wrench is dropped from a scaffold platform 78.4 m above the ground. Air resistance is ignored. How long does it take to reach the ground?
Write down the values in the question:
Δx = 78.4 m (taking down as positive)
v₀ = 0 (dropped from rest)
a = 9.8 m/s²
Write down the equation:
Δx = v₀t + ½at²
Make t the subject (with v₀ = 0):
t = √(2Δx/a)
Substitute in the values:
t = √(2 × 78.4 / 9.8)
Simplify:
t = √16 = 4.0 s
Sanity check: four times the height takes only twice the time, because the time is squared.
A ball is dropped from a window 44.1 m above the sidewalk. Air resistance is ignored. How long does it take to reach the sidewalk? Enter the time in seconds.
A coin slips from a visitor's hand at a lookout point 122.5 m above the base of a gorge. Air resistance is ignored. How long does the coin fall?
Write down the values in the question:
Δx = 122.5 m (taking down as positive)
v₀ = 0 (slips from rest)
a = 9.8 m/s²
Write down the equation:
Δx = v₀t + ½at²
Make t the subject (with v₀ = 0):
t = √(2Δx/a)
Substitute in the values:
t = √(2 × 122.5 / 9.8)
Simplify:
t = √25 = 5.0 s
A flowerpot is knocked off a balcony rail 11.025 m above the pavement. Air resistance is ignored. How long does it take to hit the pavement? Enter the time in seconds.
A maintenance worker on a skyscraper roof deck 176.4 m above the plaza drops a bolt. Air resistance is ignored. How long does the bolt fall before reaching the plaza? Enter the time in seconds.
A stone is dropped from a quarry ledge 30.625 m above the quarry floor. Air resistance is ignored. How long is the stone in the air? Enter the time in seconds.
A test mass is released from rest at the top of a 240.1 m drop-test tower. Air resistance is ignored. How long does the fall last? Enter the time in seconds.
A climber's water bottle slips from a cliff edge 99.225 m above the trail below. Air resistance is ignored. How long after slipping does the bottle reach the trail? Enter the time in seconds.