How Far III
Directions:
Show the solutions (i.e. your work) to these on a separate sheet of paper. Turn in this sheet with no marks on it when
you are through with it. (Maybe wait
until after the test?)
3.74 s +36.7 m/s 36.7 m/s 68.5 m +19.1 or 19.1 m/s 
1.
Helen Wheels launches a rocket in the air for a total of 7.48 seconds. What time did it spend going up? What is its initial velocity? What is its final velocity? How high did
it go? What is the rocket's velocity
at an elevation of 50.0 m? (Why are
there two answers?) t=7.48s it takes half of the time to
go up and half to come down so 7.48s*(1/2)= 3.74s a=v/t a=9.8
t= 3.74s 9.8 is positive in
this case because the rocket is going up 9.8*3.74s=
36.7m/s coming
down same equation but 9.8 is negative
9.8*3.74=36.7m/s s=ut+1/2at^2 u=36.7m/s t=3.74s a=
9.8m/s^2 s=68.5m v^2=u^2+2as s= 50m
u= 36.7 a= 9.8 v= 19.1 and –19.1 m/s because the rocket passes the spot on
the way up and on the way down

525 s 14.2 km 
2.
A Honda driven by Cliff Jumper going 27 m/s is 2.1 kilometers (km) behind
another Pinto driven by Ima Sloe going 23 m/s in the same direction. What time will it take the Cliff to
overtake Ima? What distance will the
Cliff travel in this time? v1=
27m/s v2= 23m/s s= 2.1 km v=s/t v= 27m/s –23m/s =4m/s Do not forget to convert km to m 2.1*1000= 2100m t=525s v=27m/s t= 525s
v=s/t s=14.2 km

12.8 m/s 24.3 m/s 8.3 m 8.0 m/s +5.1 m 
3.
Freda Dadark throws a ball up from the roof of a building at a height of 21.7
m. It strikes the ground 3.78 seconds
later. What is the initial velocity
of the ball? With what velocity does
the ball hit the ground? How high
above the building does the ball go?
What is the velocity and displacement 2.12 seconds after the ball was
released? u = ? v = ? a = 9.8 s = 21.7 t = 3.78
s = ut + 1/2at^{2}
21.7 = u(3.78) + 1/2(9.8)(3.78)^{2}
21.7  1/2(9.8)(3.78)^{2} = u(3.78)
48.3136 = u(3.78), u = 12.7813 m/s
v = u + at, v = 12.7813 + (9.8)*3.78 = 24.3 m/s
above the building u = 12.7813, v = 0
v^{2} = u^{2} + 2as, 0^{2} = 12.7813^{2} + 2(9.8)s , s = 8.33 m
Velocity and displacement at 2.12 s: v = u + at, = 12.7813 + 9.8*2.12 = 8.0 m/s
s = ut + 1/2at^{2} = 12.7813*2.12 + 1/2(9.8)*2.12^{2 }= 5.1 m

4.74 s 33.1m/s 110 m 
4.
Catona Hotinruff is ascending in a helicopter at a rate of 13.3 m/s. At an elevation of 47.0 m, she drops a
bagel out the window of the 'copter.
What time does the bagel take to reach the ground? What is its velocity of impact? How high is the helicopter when the bagel
hits the ground? V=13.3m/s s=47m a=9.8
s=ut+1/2at^2 47=13.3t+1/2*9.8t^2 t=4.74s v=u+at v=13.3+9.8(4.47) v=33.15m/s u=13.3m/s t=4.74s v=s/t s=63.042 + the original 47m
=110m

49.2 m/s 808 m 
5.
Colin Host is driving his Ferrari 345 m behind my Tercel. I am going 28.2 m/s, but the Colin
overtakes me in 16.43 seconds. How
fast is the Ferrari going? How far
does the Ferrari travel before it overtakes me? s=345m v=28.2m/s t=16.43s v=s/t v128.2=345m/16.43s v1=49.2m/s v=s/t 49.2=s/16.43 s=808m

67.1 mph 
6.
Bob White is 12.5 miles from home. If
he drives the first 3.0 miles home at 35 mph, how fast does he need to drive
the rest to average 55 mph #6
To average 55 mph, the trip home should
take V=s/t so: 55mph=12.5/t
Which means t=.2727272 hours.
The first 3 miles takes him v=s/t 35mph=3/t, t=.085714 hours Now he has 12.53 = 9.5 miles to go and .27272.085714=.141558 hours So he needs to go v = s/t = 9.5/.141558 = 67.1 mph

5.94 s 60.7 m 23.7 m/s 
7.
Justin Case fires an air rocket upward at 34.5 m/s from ground level. Unfortunately (for him) the rocket lands
on the top of a 32.0 m tall light tower on its way down. What time is the rocket in the air? How high
does the rocket go? With what
velocity does it strike the tower? u= =34.5 m/s a= 9.8 m/s s= +32 m^{} use v^{2} = u^{2} +2as so v^{2 }= (34.5)+2(9.8)(32) v= 23.73 m/s Since the rocket hits the tower on the way down then v must be negative. So now we know: u==34.5 m/s, v=23.7 m/s, a=9.8 m/s, and s==32m To find time in the air use v=u+at 23.73=34.5 + (9.8)t, t=5.94s for how high we know u=34.5 m/s, a=9.8 m/s/s, and v=0 (top) use v^{2} = u^{2} +2as 0= 34.5^{2}+2(9.8)s s=60.7m

7.17 s 1.52 s (going up) 5.66 s (going down) 
8.
Molly Fayad pops a softball up that ends up being caught by the catcher at
the same elevation as she hit it. A
spectator, using a sextant, and a range finder, determines that the ball went
63.0 m into the air at its highest point.
For what total time was the ball in the air? At what times is the ball at an elevation of 42.0 m? We know on the trip up: u=?, v=0, s=63, a=9.8 m/s/s Use v^{2} = u^{2} +2as O= us+2(9.8)(63) U= 35.139m/s positive because it starts out going up To find time in air use twice the time to the top U=35.139m/s v=0 a= 9.8 v=u+at 0= 35.139 + 9.8t t=3.5856s twice that is 7.17s s=42m and the above velovity v^2=u^2=2as v^2=35.139^2+2(9.8)(42) v=20.288m/s positive on the way up, negative on the way down going up u=35.139m/s v=20.288m/s a=9.8 v=u+at 20.288= 35.139+9.8t t=1.52s going down v=u+at 20.288=35.139+9.8t t=5.66s

6.65 m/s (6.52 is wrong) 
9.
Austin Tascious sends a bowling ball down a 16.5 m long lane, and we hear the
sound of impact 2.53 seconds later.
If the speed of sound is 343 m/s, what speed did the bowling ball
move? T=2.53s Vsound=343m/s Sound
takes v=s/t 343=16.5/t =.0481s 2.53.0481=2.482s for the ball to reach the pins the
ball must be going v=s/t 16.5/2.482 =6.65m/s

57.5 m 
10.
Ali Katz is taking a dripping paint bucket back to the store, so he holds the
paint bucket out the car's window, letting the paint drip onto the
ground. The bucket is dripping at
some unknown rate, and his car accelerates at some unknown rate, starting
from rest. If the first drop drips
when his car's velocity is zero, the second drop is 2.3 m down the road, how
far is the sixth drop down the road? Second
drop t2=? A=? s2=2.3 We
also know the fifth drop
t5=4t2 (it dripped four
times later than the second drop
a=? s=? S=ut+1/2at^2 since u=0 s=1/2at^2 A=B &
C=D S2=1/2at2^2 and s5=1/2a(4t2)^2 then A/C=B/D Both
“a” s are the same so we can solve 2.3m=1/2a(t2)^2 = (t2)^2 = 1 s5 =1/2a(4t2)^2 16(t2)^2
16 2.3/s5 =
1/16 s5= 2.3*16 =
36.8m 