1. Falling Objects worksheet assistance
Physics
Falling Objects worksheet assistance

2. 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 positive

3. Question #1, continued The simplest equation that I can find is:
vf2 = vi2 + 2ay
vf2 = 0 + 2(9.81)(343)
vf2 =
vf = 82 m/s (yes, I rounded)

4. 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
vi = 9.98 m/s
vf = ? (at the top of the house)
a = m/s2 (since it is opposite the direction of travel)

5. Question #2, continued
Since there is no time element, I will again use:
vf2 = (9.98)2 + 2(-9.81)(4.88)
vf2 = (-9.81)(4.88)
vf2 =
vf2 = 3.9
vf = 1.97 m/s

6. 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
vf = 0 m/s (at the top of the jump)
a = 9.81 m/s2
So we can determine the initial velocity that a flea jumps with

7. Question #9, continued vf2 = vi2 + 2ay
0 = vi2 + 2(-9.81)(.21) [I had to switch from cm to m to match the acceleration]
0 = vi2 + 2(-9.81)(.21)
0 = vi
4.12 = vi2
vi = 2.03 m/s

8. 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 + vit + ½ at2
.07 = t + ½ (-9.81)t2
.07 = 2.03t t2
UH OH, I smell a quadratic equation coming up!
4.905t2 – 2.03t = 0
( ) /9.81 AND ( ) /9.81
t = .38s AND .04s
The two times represent on the way up and down; the minimum time is .04s