projectile motion
Summary
Projectile motion is the curved, two-dimensional path of an object launched into the air and moving under gravity, with air resistance neglected. Horizontal and vertical motions are independent: horizontal velocity is constant, while vertical velocity changes at g = 9.8 m/s² downward.
Detail
Meaning: A projectile has gravity as its net force once launched. Horizontally the acceleration is zero, so vx stays constant. Vertically the acceleration is g downward, so vy changes at a steady rate. The two motions share only the time, and the path is a parabola. At the peak of an angled launch, vy = 0 but vx is not.
Equation: y = y₀ + v₀sinθ·t − ½gt², with x = v₀cosθ·t, where x and y are position (m), y₀ is initial height (m), v₀ is launch speed (m/s), θ is the launch angle above horizontal, t is time (s), and g = 9.8 m/s².
On the MCAT: Expect a ball kicked, thrown off a cliff, or fired horizontally. Resolve the launch velocity into components, find the time from the vertical motion, then use that time for the horizontal distance. A dropped object and a horizontally launched one from the same height land together. For equal launch and landing heights, range is greatest at 45°.
Common confusion: Students think acceleration is zero at the top of the path. Only vy is zero there; acceleration is still g downward. Another error is thinking a horizontal force sustains the horizontal motion. Without air resistance, no horizontal force is needed, and mass does not change the trajectory.
Sources
- Physics (Giancoli)
- Fundamentals of Physics (Halliday, Resnick, Walker)
- University Physics (Young and Freedman)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.