Kinematics and projectile motion

Kinematics describes motion without worrying yet about what causes it. We track position, velocity, acceleration, and time so we can make clean predictions about paths and flight times.

The big idea

For projectile motion, the horizontal and vertical directions can be analyzed separately. Horizontal velocity stays constant while vertical velocity changes because of gravity.

Horizontal

x = v_x t

No horizontal acceleration

Vertical

y = v_y t - 0.5 g t^2

Gravity changes vertical motion

Velocity

v_y = v_{y0} - g t

Launch speed sets the starting components

How to solve a projectile problem

1. Resolve the launch speed into horizontal and vertical components.
2. Use the vertical motion to find time of flight or maximum height.
3. Use the horizontal component with that time to find range.
4. Check whether the answer has the right units and scale.

Worked example

A ball is launched at 20 m/s and 30 deg above horizontal. First compute the components: v_x = 20 cos(30 deg) and v_y = 20 sin(30 deg). Then use the vertical motion to find the total flight time, and multiply that time by v_x to get the range.

Interactive lab

Projectile Motion

Initial Speed: 20 m/s

Launch Angle: 45 deg

Initial Height: 0 m

Time of Flight

2.89 s

Max Height

10.20 m

Range

40.82 m

Initial Vx

14.14 m/s

Next step

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Quick reference

Gravity: g = 9.8 m/s^2
Time of flight: t = 2 v_y / g
Range: R = v_x t