Physics Falling Objects worksheet assistance - PowerPoint Presentation

Slide1

Physics

Falling Objects worksheet assistanceSlide2

Question #1

The John Hancock Center in Chicago is the tallest building in the

United States

in which there are residential apartments. The Hancock Center

is 343

m tall. Suppose a resident accidentally causes a chunk of ice to

fall from

the roof. What would be the velocity of the ice as it hits the

ground? Neglect

air

resistance

y = 343 m

vi = 0 m/s (when it first starts to fall)

vf = ?

a = 9.8 m/s2

NOTE: I choose the frame of reference where down is positiveSlide3

Question #1, continued

The simplest equation that I can find is:

v

f

2

= v

i

2

+ 2ay

v

f

2

= 0 + 2(9.81)(343)

v

f

2

= 6729.66

v

f

= 82 m/s (yes, I rounded)Slide4

Question #2

Brian

Berg of Iowa built a house of cards 4.88 m tall. Suppose

Berg throws

a ball from ground level with a velocity of 9.98 m/s straight

up. What

is the velocity of the ball as it first passes the top of the card house

?

y = 4.88 m

v

i

= 9.98 m/s

v

f

= ? (at the top of the house)

a = -9.81 m/s

2

(since it is opposite the direction of travel)Slide5

Question #2, continued

Since there is no time element, I will again use:

v

f

2

= (9.98)

2

+ 2(-9.81)(4.88)

v

f

2

= 99.6 + 2(-9.81)(4.88)

v

f

2

= 99.6 + -95.7

v

f

2

= 3.9

v

f

= 1.97 m/sSlide6

Question #9

A common flea is recorded to have jumped as high as 21 cm.

Assuming that

the jump is entirely in the vertical direction and that air resistance

is insignificant

, calculate the time it takes the flea to reach a height of 7.0 cm

Initially, it looks like we don’t have enough information

However, there is some implied information here

Consider the first jump:

y = 21 cm

v

f

= 0 m/s (at the top of the jump)

a = 9.81 m/s

2

So we can determine the initial velocity that a flea jumps withSlide7

Question #9, continued

v

f

2

= v

i

2

+ 2ay

0 = v

i

2

+ 2(-9.81)(.21) [I had to switch from cm to m to match the acceleration]

0 = v

i

2

+ 2(-9.81)(.21)

0 = v

i

2

-4.12

4.12 = v

i

2

v

i

= 2.03 m/sSlide8

Question #9, part 3

Now we know the initial velocity

Since we don’t know (and it doesn’t ask for the velocity at 7 cm, and only the time, we’ll use:

x = xi +

v

i

t

+ ½ at

2

.07 = 0 + 2.03t + ½ (-9.81)t

2

.07 = 2.03t -4.905t

2

UH OH, I smell a quadratic equation coming up!

4.905t

2

– 2.03t + .07 = 0

(2.03 + 1.65) /9.81 AND

(2.03 - 1.65) /9.81

t = .38s AND .04s

The two times represent on the way up and down; the minimum time is

.04s