Physics / Unit 2: Vectors and Motion in Two Dimensions
2.3 Horizontally Launched Projectiles
Notes
A projectile moves only under gravity. Its horizontal and vertical motions are independent.
- Horizontal: no acceleration, so $x = v_x t$.
- Vertical: free fall from $v_y = 0$, so $\displaystyle y = \frac{1}{2}gt^2$.
- The time in the air depends only on the height, not on the horizontal speed.
- Example: a ball rolls off a 19.6 m cliff at $5 \text{ m/s}$. $\displaystyle t = \sqrt{\frac{2(19.6)}{9.8}} = 2 \text{ s}$; it lands $5 \times 2 = 10 \text{ m}$ from the base.
Practice
One ball is dropped and another is fired horizontally from the same height at the same moment. Ignoring air, which lands first?
Both start with zero vertical velocity and fall with the same acceleration.
A marble rolls off a table 1.225 m high. How long is it in the air?
$\displaystyle t = \sqrt{\frac{2(1.225)}{9.8}} = \sqrt{0.25} = 0.5 \text{ s}$.
A package is dropped from a plane flying horizontally at $50 \text{ m/s}$. It falls for 4 s. How far does it travel horizontally? (Ignore air.)
It keeps the plane's horizontal speed: $50 \times 4 = 200 \text{ m}$.
Ready for more? Take the Unit 2 test.