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Projectile motion Remember Newton’s 1st law of motion If there is no force acting on an object there is no acceleration, so the object will be stationary or will move at a constant velocity.

Definition of a projectile Any object moving through air without its own source of power and only under the influence of gravity… eg: a golf ball after being hit.

Compare a ball rolling off a desk to one being dropped The balls land at the same time because the force of gravity is the same on both. The rolled ball continues moving forward at the same speed as on the desk: there is no horizontal force to slow it down.

Key physics ideas for projectiles Divide the story into horizontal and vertical directions. There are no horizontal forces acting so the velocity is constant and we use the equation v = d/t. The only vertical force is gravity so we know the acceleration is 9.8ms-2. Time of flight is the only thing common to the vertical and horizontal movements. Use the five equations of motion.

Solving Projectile problems: the first type… Facts about simple vertical projectiles Throwing something straight up or down Acceleration is -9.8ms-2 on the way up and +9.8ms-2 on the way down Velocity is 0ms-1 at the top of the motion

Q: A tennis player throws up a ball at 5. 8ms-1 for a serve Q: A tennis player throws up a ball at 5.8ms-1 for a serve. What is the maximum height the ball reaches? Fill in the information you know Vi = Vf = a = d = Choose an equation of motion Substitute and solve Use the problem and common sense Vi = 5.8 ms-1 Vf = 0 ms-1 a = -10 ms-2 d = ? Vf2 = Vi2 +2ad 0 = 5.82 + 2(-10)d d = 1.7m

Q: A tennis ball is thrown up at 3. 9ms-1 Q: A tennis ball is thrown up at 3.9ms-1. How long does it take to reach its maximum height? Q: A rock is dropped off a cliff 75m high. How long does it take to reach the bottom of the cliff? What is its speed after 2s? Vi = 3.9 ms-1, Vf = 0ms-1, a = -10 ms-2, t = ? Vf = Vi + at 0 = 3.9 +-10t t = 0.398s d = 75 m, Vi = 0 ms-1, a = -10 ms-2 d = Vit + 1/2at2 75 = 1/2 (-10)t2 t = 3.9s Vf = Vi + at = 0 +10x2 = 20ms-1

Solving projectile problems: the second type Half projectiles At position A the velocity is only horizontal At position B the horizontal velocity is the same but there is a vertical component A B Range

Q: A person fires a gun horizontally from the top of a cliff 70m high Q: A person fires a gun horizontally from the top of a cliff 70m high. The bullet travels out at 100ms-1. Two possible Q… What is the time to the bottom? Since time is the dame vertically or horizontally, use either vertical or horizontal, eg: vertically, Vi = 0 ms-1, a = 10 ms-2, d = 70 m d = Vit + 1/2at2 70 = 0 + ½(10) t2 t = 3.7s What is the range? Must use the horizontal information, Vi = 100 ms-1, a = 0 ms-2, t = 3.7 s d = vt = 100(3.7) = 370m

Q: A duck shooter fires a bullet horizontally at 80ms-1 to hit a duck Q: A duck shooter fires a bullet horizontally at 80ms-1 to hit a duck. They miss, and the bullet comes down 1.8m to hit the ground. Find the time for the bullet to hit the ground and the distance away from the shooter that it lands. Q: A food crate is dropped from a plane flying horizontally at 160ms -1. If the crate takes 12s to hit the ground, from how high was it dropped. How far does the crate travel horizontally from the point where it was dropped?