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Example Problems

Example Problems. Projectile Motion. A ball is thrown horizontally from the top of a building 47.7 m high. The ball strikes the ground at a point 108 m from the base of the building. A. Find the time the ball is in motion. B. Find the initial velocity

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Example Problems

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  1. Example Problems Projectile Motion

  2. A ball is thrown horizontally from the top of a building 47.7 m high. The ball strikes the ground at a point 108 m from the base of the building. • A. Find the time the ball is in motion. • B. Find the initial velocity • C. Find the x component of the velocity just before it hits the ground • D. Find the y component of the velocity just before it hits the ground

  3. The time the ball is in the air • Is gravity effecting it? • Yes, use the vertical equations. • D=1/2gt2 • √2d/g • 2*47.7/9.8 • √9.7=3.12s

  4. Initial Velocity of the ball • V=d/t • 108/3.12 • V=34.6

  5. Find the x component of the velocity just before it hits the ground • The same as the initial velocity

  6. Find the y component of the velocity just before it hits the ground • V=gt • V=-9.8*3.12 • V=-30.5765 m/s • ***Remember it is falling down and gravity would be negative

  7. An arrow is shot at a 33⁰ angle with the horizontal. It has a velocity of 54 m/s • A. How high will it go? • B. What horizontal distance will it travel?

  8. Vertical speed Horizontal speed • 54m/s • 33⁰ vy Vx Sin 33 =y/54 Sin 33 *54 =29.41 m/s • Cos 33=x/54 • Cos 33 * 54= 45.28m/s

  9. Look at your vertical equations • D=1/2gt2 • V=gt • Let’s combine these two equations using substitution method. • t=v/g • d=1/2 g(v/g)2 • d=44.13 m

  10. Now lets solve for the horizontal distance. • We solved for the horizontal velocity and now we need to find an equation for the horizontal distance. • D=vt and because of the trajectory we need to use twice the time from the previous problem.

  11. A descent vehicle landing on the moon has a vertical velocity vector toward the surface of the moon of 31.6 m/s. At the same time, it has a horizontal velocity of 53.2 m/s. • At what speed does the vehicle move along its descent path? • At what angle with the vertical is its path?

  12. At what speed does the vehicle move along its descent path? • 31.6 m/s R • 53.6 m/s • a2+b2=c2

  13. At what angle with the vertical is its path? • 31.6 m/s R • θ=? • 53.6 m/s tan θ=o/a Θ=tan-1 (o/a)

  14. Janet jumps off a high diving platform with a horizontal velocity of 2.83 m/s and lands in the water 2.2s later. • A. How high is the platform? • B. How far from the base of the platform does she land?

  15. A is asking for the vertical distance • D=1/2gt2

  16. B is asking for horizontal distance • D=vt

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