Two dimensional kinematics and projectile motion
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Examples
Lessons
- Type 1 – Projectile at an Upward Angle
A projectile is launched from the edge of a cliff 100 m above ground level with an initial speed of 20 m/s at an angle of 35° above the horizontal. Find:
- the horizontal and vertical components of the launch speed.
- the velocity vector at the maximum height.
- the maximum height above the cliff top reached by the projectile.
- the time taken to reach the maximum height.
- the projectile's time of flight.
- the projectile's range.
- the projectile's impact velocity (magnitude and direction) with the ground.
- Type 2 – Projectile at a Downward Angle
A hammer slides down a roof sloped at 35° reaching a speed of 6.2 m/s before falling off.
- Type 3 – Horizontally Launched Projectile
A ball rolls off a cliff at 8 m/s and hits the ground with a speed of 25 m/s.
- Projectile Returning to the Same Height – Level Range Formulas
Prove: Level Range Formulas - time of flight:
- horizontal range:
- Projectile Returning to the Same Height – Level Range Formulas
A football is kicked at an angle 65° with a velocity of 18 m/s. Determine the football's range and time of flight: