Two dimensional kinematics and projectile motion  Kinematics
Two dimensional kinematics and projectile motion
Lessons
Notes:
Notes:
Shortcut: Level Range Formulas for projectile returning to its original height:
 horizontal range: $d_x = \frac{v_i^2 \cdot sin2\theta}{g}$
 time of flight: $t=\frac{2v_i \cdot sin\theta }{g}$

1.
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:

2.
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.

3.
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.

5.
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: