Practice
Projectile motion
Split a launch into horizontal and vertical motion: time of flight, maximum height, range and a ball rolling off a table.
The skill
A projectile is two one-dimensional motions sharing one clock. Split the launch velocity into components, and . Horizontally nothing accelerates the object, so stays constant; vertically the acceleration is , downward. Solve whichever direction gives you the time, then carry that time to the other direction. The usual error is letting the horizontal speed change the fall time: a ball rolled off a table and a ball dropped from the same height land together.
A worked example
A ball rolls off the edge of a horizontal tabletop 0.70 m above the floor, moving horizontally at 2.8 m/s as it leaves. Air resistance is negligible. Use g = 10 m/s².
How far from the edge of the table, measured horizontally, does the ball hit the floor, in meters? Give your answer to three significant figures.
Solution
- Vertically the ball starts with no velocity and falls 0.70 m: 0.70 = 1/2 (10) t², so t = 0.374 s.
- Horizontally nothing accelerates the ball, so it keeps 2.8 m/s for that whole time: x = (2.8)(0.374) = 1.05 m.
Answer: 1.05