Projectile Motion - Sumulong Memorial High School

LESSON : PROJECTILE MOTION: A TWO DIMENSIONAL MOTION FOCUS POINTS: Describe the horizontal and vertical motions of a projectile. Investigate the relationship between the angle of release and the height and range of the projectile....

LESSON : PROJECTILE MOTION: A TWO DIMENSIONAL MOTION FOCUS POINTS: Describe the horizontal and vertical motions of a projectile. Investigate the relationship between the angle of release and the height and range of the projectile. PROJECTILE MOTION is a form of motion where an object moves in parabolic path; the path that the object follows is called its trajectory. PROJECTILE Is an object that is initially thrown into the air and continues to move on its trajectory acted upon by the gravity. You will understand what is happening to the projectile by analyzing its velocity as its travels its trajectory. Elements of Projectile Motion When launching the projectile, it is given by an initial velocity, at an initial angle. As it travels through the air, it displaces in two dimensions, along the horizontal, and along the vertical. What goes up, returns back to earth and hits the earth or a target with a final velocity.  We usually solve for three factors in El projectile motion: em Pr en oj time of flight – the entire duration e ts M while the projectile is in its trajectory ot ctil of io e Range – the maximum horizontal n distance travelled by the projectile. Maximum height – maximum vertical displacement travelled by the projectile in its trajectory.  Initial Velocity- The initial velocity can be expressed as x components and y components. Co K Acceleration - In projectile motion, m ey po there is no acceleration in the ne n ts horizontal direction. The acceleration, aa, in the vertical direction is just due to gravity, also known as free fall. Maximum Height - The maximum height is reached when vf=0.  Through the Flight 1. We will neglect the effect of air resistance on the body. 2. We can separate the displacement and velocity to its x and y components. Along the Horizontal 1. The x component of the velocity is always constant throughout the range. 2. the horizontal displacement (X) follows a linear motion. Co Pr tion th Mo nd oje e Along the Vertical 1. The y-component behaves as free-fall, and thus, only affected by the acceleration due to gravity. i ti 2. Since our velocity is usually in an upward direction, from 0 to less on tile than 90 degree with respect to the horizontal, then our convention is upward positive, downward negative. so c 3. Before reaching the maximum height, gravity acts against the velocity, slowing it down until it reaches zero. This part is equivalent f to a p-t graph where velocity is positive, but acceleration is negative. 4. After reaching the maximum height, gravity is in the same direction as the velocity, speeding up.  Co th nd When the 1.The x component of the e i Pr tio Vertical velocity is always constant. M oj ns Displace 2.The y component of the ot e io cti of ment is at velocity is zero. n le its 3. the acceleration is still (g) Maximum and not zero. Problem #1 : A pool ball leaves a 0.60-meter high table with an initial horizontal velocity of 2.4 m/s. A.)Predict the time required for the pool ball to fall to the ground and B.)the horizontal distance between the table's edge and the ball's landing location. Problem #: A ball is kicked horizontally off a 32 meter high building and lands a distance of 35 meters from the edge of the building. Determine the initial horizontal velocity of the ball. Problem #: An object is moving horizontally at 70 m/s on a cliff that is 50 m high. What is the time of flight? What is the horizontal distance or range? Problem #: A ball is thrown with an initial Velocity of 32.7m/s off the top of an elevated hill with an angle of 20 degree. If the time it takes to reach the ground is 9.50 seconds. What is the height of the hill? Problem #: A rocket is fired at 32 m/s in a direction that makes a 40° upward angle with the horizontal. a) What is the maximum height that the object can reach? b) What is the object's entire flight time (from launch to contact with the ground)? c) What is the object's horizontal range? Problem #3 :