Lecture 17 - University of Oklahoma

[Pages:14]Physics 2514

Lecture 17

P. Gutierrez

Department of Physics & Astronomy University of Oklahoma

Physics 2514 ? p. 1/14

Finish the discussion on projectile motion

Discuss the range formula; Consider a couple of examples.

Goals

Physics 2514 ? p. 2/14

Projectile Motion

Let's consider how far a projectile travels;

Assume that it returns to the same height (y = y0)

Derive "Range Formula"

y

-

y0

=

g -

2v02x

(x

-

x0)2

+

v0y v0x

(x

-

x0)

0

=

g -

2v02x

(x

-

x0)2

+

v0y v0x

(x

-

x0)

(x - x0)

=

2 g v0xv0y

=

v02 sin(2) g

2v0xv0y = 2v02 sin cos = v02 sin(2)

Physics 2514 ? p. 3/14

Projectile Motion

Two comments on the range formula

Distance

=

(x -

x0)

=

v02 sin(2) g

Maximum range when = 45

d v02 sin(2) = 2v02 cos(2) = 0 = 45

d

g

g

Since sin(180 - ) = sin sin[2(90 - )] = sin(2)

therefore the range is same for and 90 -

Physics 2514 ? p. 4/14

Projectile Motion

Physics 2514 ? p. 5/14

Projectile Motion

All objects fall at the same rate independent of there mass and horizontal motion.

Physics 2514 ? p. 6/14

Clicker

A 100 g golf ball rolls off a table and lands 2 m from the base of the table. A 200 g ball rolls off the same table with the same speed. What distance from the base of the table does it land? (Ignore air resistance.)

1. < 1 m 2. 1 m 3. Between 1 and 2 m 4. 2 m 5. Between 2 and 4 m

Physics 2514 ? p. 7/14

Example 1

A supply plane needs to drop a package of food to a person stranded on a desert island. The plane flies 100 m above the island at a speed of 150 m/s. How far short of the target should it drop the package.

150 m/s

PSfrag replacements

D 100 m

Physics 2514 ? p. 8/14

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