Physics 2211, Spring 2005

1
Physics 2211 Lecture 13

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

2
ExampleProjectile Motion Basketball Free
Throws(or life at the charity stripe)

• Projectile motion for fun and profit!

3
ExampleProjectile Motion Basketball Free
Throws

• If the basketball is thrown at 55 degrees above
  the horizontal, what must its initial speed be
  for the foul shot to go in?

4
Example
Constant Acceleration Problem

• Choose y axis up.
• Choose x axis parallel to the floor in the
  direction of the basket.
• Choose the origin (0,0) to be at the ball.

5
Example

• Find the x and y components of initial velocity

6
Example
7
Problem

• Barry Bonds clobbers a fastball toward
  center-field. The ball is hit 1 m (d ) above the
  plate, and its initial velocity is 36.5 m/s (v0 )
  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 Barry get a home run?

8
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.
• The ball is hit at t 0, x x0 0 and y y0
  d.

Kinematics equations are
9
Problem

• Use geometry to figure out v0x and v0y

10
Problem

• The time to reach the wall is t D / v0x
  (easy!)
• We have an equation that tells us y(t) d v0y
  t - g t2/ 2
• So, were done....now we just plug in the
  numbers
• Find
• v0x 36.5 cos(30o) m/s 31.6 m/s
• v0y 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 3.0 m high, Barry gets the
  homer!!