Projectiles Cf E Higher Physics Projectiles A projectile

Projectiles Cf. E Higher Physics

Projectiles �A projectile is an object that moves with a constant horizontal velocity whilst simultaneously accelerating vertically due to gravity. Some examples of projectiles are:

Projectiles from N 5 Example A ball is kicked off a cliff at 10 m s-1. It lands 4 seconds later. a) Calculate the horizontal distance it travels before it lands. b) Calculate the height of the cliff. a) d =v x t = 10 x 4 = 40 m b) s = ut + (½ a t 2 ) = (1/2 x 9. 8 x 42) = 78. 4 m This could only be done in N 5 by working out final vertical velocity and then the area under the vertical “speed time” graph In this question we don’t have to worry about positive and negative directions vertically as there is no change in direction, so downwards is positive, (everything is positive!)

Projectiles(2) �If an object follows a full parabolic path (up and down) it needs a bit more work……. . but there is a series of steps you can use to solve these questions 40 ms-1 50° Step 1: Split the initial velocity of the ball into its horizontal and vertical components. Horizontal component: uh = u cos θ Vertical component: uv = u sin θ Q. A golfer hits a shot with an initial velocity of 40 m s 1 at 50° to the horizontal. Calculate the horizontal distance travelled by the ball until it first hits the ground. 40 ms-1 uv = 40 sin 50 = 31 m s-1 50° uh = 40 cos 50 = 26 m s-1 These components are needed for step 2

Projectiles (2) continued Step 2: split the page Vertical 40 ms-1 Horizontal s= u = 31 m s-1 v = 0 (at max height) a = - 9. 8 m s-2 t= s= u = 26 m s-1 t = 6. 4 s uv = 40 sin 50 = 31 m s-1 50° uh = 40 cos 50 = 26 m s-1 Step 3: time is the key! – find the time taken for the ball to reach its maximum height vertically. This can be doubled to find the total time of flight. Step 4: find the horizontal distance gone. Total time of flight = 6. 4 seconds

Tips for projectile questions �Split the initial velocity into it’s horizontal and vertical components �“cos” for across, “sin” if you climb. �Split the page �Keep the vertical and horizontal velocities separate. �Vertical velocity is zero at the maximum height. �Vertical acceleration = - 9. 8 m s-2 (watch your sign convention…up is positive!) �Total time of flight = 2 x time to go up (if it returns to the same height) �You can use “distance = speed x time” horizontally. (Try plenty of examples)

2016 past paper question