Projectile Motion Projectile Motion A projectile is an object moving through the air only under the force of gravity Free fall is a special case of projectile motion A projectile’s path through space is called its trajectory Projectile Motion • An object may move in both the x and y directions simultaneously • The form of two-dimensional motion we will deal with is called projectile motion Projectile Motion Possible Preconceptions to Correct Here are some misconceptions about Projectile Motion that you may need to correct: • Wrong: The curved motion of a projectile is very different from common one-dimensional motions. • Wrong: An object at rest will drop to the ground faster than the same object moving horizontally at high speed. • Wrong: At the top of its trajectory, the velocity of a projectile is always momentarily zero. Projectile Motion Analyzing projectile motion: Separate the horizontal and vertical parts of the motion Two general cases • a projectile launched horizontally • a projectile launched at an angle Projectile Motion Projectile launched horizontally calculating position Projectile Motion Projectile launched horizontally calculating position Projectile Motion Projectile launched horizontally calculating position Projectile Motion Projectile launched horizontally calculating position Projectile Motion The Components of the Velocity • We know that the vertical motion of a projectile is the same as its motion would be in free fall. Therefore, the vertical component of its velocity changes by 10 m/s (actually 9.8 m/s) each second. Projectile launched horizontally calculating velocity Projectile Motion The Components of the Velocity - 2 • We also know that the horizontal motion of a projectile is at constant velocity - if it starts at 5 m/s (for instance), the horizontal component of its velocity remains 5 m/s until it hits the ground. Projectile Motion Question: "A bowling ball rolls off a horizontal cliff 80 meters high with a speed of 5 m/s. How long will it take the bowling ball to land, and how far from the base of the cliff will it land?" Projectile Motion How long will it take to land? y = 1/2 gt2 t = sqrt (2y/g) t = sqrt (2 x 80m / 10m/s2) = sqrt (16 s2) = 4 seconds How far from the base of the cliff will it land? The velocity is constant in the horizontal direction therefore: x = vt = 5m/s times 4 s = 20 meters Projectile Motion Projectile Motion Finding the Velocity from its Components If you know the horizontal and vertical velocity components, you can find the magnitude of the projectile's velocity and the projectile's direction of motion as follows: 1. Draw the horizontal and vertical velocity components (to scale) starting from a common point. 2. Draw 2 more sides to complete a rectangle. Projectile Motion Finding the Velocity from its Components -2 3. The velocity of the projectile is the diagonal of the rectangle that starts at the point from which you drew the velocity components. 4. You can determine the magnitude of the velocity by measuring the scale drawing or using the Pythagorean Theorem. You can determine the angle that the velocity makes with the horizontal (or vertical) by measuring the scale drawing with a protractor, or using trigonometry. Projectile Motion Projectile launched at an angle calculating position Projectile Motion Projectile launched at an angle calculating position Projectile Motion Projectile launched at an angle calculating position Projectile Motion Projectile launched at an angle calculating position Projectile Motion Projectile launched at an angle calculating position Projectile Motion Projectile launched at an angle calculating position Projectile Motion Projectile launched at an angle calculating position Projectile Motion Projectile launched at an angle calculating position Projectile Motion Projectile launched at an angle calculating position Projectile Motion Projectile launched at an angle calculating position Projectile Motion Projectile launched at an angle calculating position Projectile Motion Projectile launched at an angle calculating position Projectile Motion Projectile launched at an angle calculating position Projectile Motion Projectile launched at an angle calculating position Projectile Motion Example problem
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