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Projectile Motion

Projectile Motion. Vectors and Scalars. A Vector is a measurement that has both a magnitude and a direction. Ex. Velocity, Force, Pressure, Weight A Scalar is a measurement that just has a magnitude. Ex. Speed, Mass, Time (does time have a direction? Hmmm….). Vector Addition.

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Projectile Motion

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  1. Projectile Motion

  2. Vectors and Scalars • A Vector is a measurement that has both a magnitude and a direction. • Ex. Velocity, Force, Pressure, Weight • A Scalar is a measurement that just has a magnitude. • Ex. Speed, Mass, Time (does time have a direction? Hmmm….)

  3. Vector Addition • If two vectors are going in the same direction, then the magnitudes are added. • If two vectors are going in opposite directions, then their components can be subtracted. • If there is a angle between them, then trigonometry needs to be used. • If the angle is 90o then use the Pythagorean Theorem (a2 + b2 = c2)

  4. Drawing Vector Diagrams • Draw the component of the first vector by drawing an arrow (should be to scale). • From the end of the first arrow, draw the second component as an arrow. • Repeat for each additional component. • Once all components are drawn, draw a third arrow from the base of the first component to the tip of the last component. This is the resultant. • The resultant is the direction that the object is moving or being changed in. • The parallelogram method works too!

  5. Trigonometry • Remember SOHCAHTOA? If not remember it now! • SOH = sinθ = opposite / hypotenuse • CAH = cos θ = adjacent / hypotenuse • TOA = tan θ = opposite / adjacent • This only works for right triangles • The opposite and adjacent refers to the length of the sides next to or across from the angle being measured.

  6. Projectile Motion • What if an object is not fired straight up, or straight down? • What is the acceleration? • When? • Does that change the motion in every direction?

  7. Math of projectiles • The first step in attacking a projectile motion problem is to determine the x and y components of its velocity. • Use SOHCAHTOA to determine those components. • Next separate the problem into the x direction and the y direction. • What is your acceleration in the x? Always? • What is your acceleration in the y? Always?

  8. Math of projectiles continued • Determine the total flight time by determining the time in the y-direction. • Apply that term to the x-direction to determine the distance. • If there is no initial y-component to the velocity, then the problems are simplified! • If there is no initial x-component to the velocity, then it’s a freefall.

  9. Satellites • Satellites are in a constant state of freefall. • That is why they feel no effects of gravity even though the Earth still has a rather large gravitational force at those small distances. • Satellites have a large x-component of velocity, so they fall “around” the Earth and never hit the ground. • Molecular friction does slowly slow the satellite’s x-component down so the orbits degrade. That’s why they come back!

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