Projectile Motion

Example: A stone is thrown horizontally at 15 m/s. It is thrown from the top of a cliff that is 44 m high. a) How long does it take the stone to reach the bottom of the cliff? b) How far from the base of the cliff does the stone strike ground?

• Horizontal velocity is constant 
• downward accerlation = gravity = 9.8 m/s^2

   a) d = 1/2 a t ^2, 44 m  = 1/2 (9.8 m/s^2) t ^2

       solve for t = 3 sec

   b) dH = vH * t,  (15 m/s) (3 sec) = 45 m 

Example: A cannon fires a cannon ball at an angle of 50 degrees with the horizontal. The velocity of the cannon ball as it leaves the muzzles of the cannon is 450 m/s. a) What is the vertical velocity? b) What is the horizonal velocity? c) How long is the cannon ball in the air? d) How far does the cannon ball land from the cannon? e) How high is the cannon ball at the top of the trajectory?

     a) Sin 50° = Vv / 450, Vv = 344.7 m/s

     b) Cos 50° = Vh /450, Vh = 289 m/s constant

     c) Sf = Si + at, 0 = 344.7 m/s + (-9.8 m/s^2) t

         solve for t = 35 s, time up + time down = 70 s

     d) dH =  Vh * t,  289 (70) = 20230 m

     e) dv = 1/2 (- 9.8 m/s^2) (35 s)^2 = 6002.5 m