Physics 2211: Lecture 7 Todays Agenda

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Physics 2211 Lecture 7Todays Agenda

• More 2-D, 3-D Kinematics, Projectile Motion
• Basketball example
• Baseball example

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Constant Acceleration
Choose y axis up. Choose x axis along the floor
in the direction of the basket. Choose the origin
(0,0) to be at players feet (under ball).
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Problem

• Mark McGwire clobbers a fastball toward
  center-field. The ball is hit 1 m (yo ) above
  the plate, and its initial velocity is 36.5 m/s
  (v ) at an angle of 30o (?) above horizontal.
  The center-field wall is 113 m (D) from the plate
  and is 3 m (h) high.
• What time does the ball reach the fence?
• Does Mark get a home run?

v
h
?
y0
D
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Problem...

• Choose y axis up.
• Choose x axis along the ground in the direction
  of the hit.
• Choose the origin (0,0) to be at the plate.
• Say that the ball is hit at t 0, x x0 0
• Equations of motion are
• vx v0x vy v0y - gt
• x vxt y y0 v0y t - 1/ 2 gt2

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Problem...

• Use geometry to figure out v0x and v0y

g
Find v0x v cos ?. and v0y v sin ?.
y
v
v0y
?
y0
v0x
x
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Problem...

• The time to reach the wall is t D / vx
  (easy!)
• We have an equation that tell us y(t) y0 v0y
  t a t2/ 2
• So, were done....now we just plug in the
  numbers
• Find
• vx 36.5 cos(30o) m/s 31.6 m/s
• vy 36.5 sin(30o) m/s 18.25 m/s
• t (113 m) / (31.6 m/s) 3.58 s
• y(t) (1.0 m) (18.25 m/s)(3.58 s) -
  
  (0.5)(9.8 m/s2)(3.58 s)2
• (1.0 65.3 - 62.8) m 3.5 m
• Since the wall is 3 m high, Mark gets the homer!!

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Recap for today

• Two 2-D projectile problems
• For next time Read Chapter 4.1 - 4.4 in Tipler.