Question

The first peak of a roller coaster is 55m above the ground. The 1200 kg car starts from rest and goes down the hill and up the second hill which is 30m high. How fast is the car traveling at the top of the second hill?

Answer 1

wt do u wanna know frm this math is not clear to me

Answer 2

now i m trying to solve ur problem in my own way

Answer 3

the final velocity of the roller coaster after coming frm 1st pick is

Answer 4

\[v ^{2}=u ^{2}+2gh\]

Answer 5

here u=0, g=10m/s, h=55m

Answer 6

\[or, v ^{2}=0^{2}+2 \times 10 \times 55\]

Answer 7

2,200 m/s is the answer?

Answer 8

\[or, v=\sqrt{2 \times 10 \times 55}=33ms ^{-1}\]

Answer 9

so the answer is 2,200 m/s

Answer 10

still not

Answer 11

now then this question uses your good old. KE+PE = KE+PE.
since there is no work done from external force,
the change in KE = change in PE
\(\frac{1}{2}mv^2=mg(h-h_o)\)
rearranging,
\(v=\sqrt{2g(h-h_o)}\)
i.e. not 2200
do you need further help?

Answer 12

we hv to find out the velocity of the roller coaster when it is on the 2nd pick

Answer 13

yes is \[v=\sqrt{2g(h-h _{o})}\] the answer to the problem?

Answer 14

ah ok. soo im lost xD

Answer 15

@shadow............. ur system is easier than mine

Answer 16

yup, derived from your original equation.
mechanical energy is conserved.
\(KE_i + PE_i =KE_f +PE_f\)
rearranging,
\(PE_f - PE_i =KE_f -KE_i\)
since \(KE_i\) =0, (the body starts from rest)
\(mgh-mgh_o=\frac{1}{2} mv^2\)
rearranging again,
\(v=\sqrt{2g(h-h_o)}\)

Answer 17

ok so we are trying to find \[v _{f}\] rite?

Answer 18

yup! :)

Answer 19

Note:The entire journey has so other force acting on it except a conservative force, gravity.
So, Mechanical energy is conserved.

Answer 20

so how do we find \[v _{f}\]

Answer 21

use your equation for kinetic energy and potential energy. the one you normally post after your questions.

Answer 22

im still lost..

Answer 23

here h=55m

Answer 24

\[h _{0}=30m\]

Answer 25

so i have to find the first velocity first before ifind the other velocity on the 2nd peak?

Answer 26

g=9.8m/s

Answer 27

yes. Now, the first velocity is zero, though. so, initial KE=0

Answer 28

so the equation Shadowys gave me the v=22.14m/s?

Answer 29

i think the result will b 2214cm/s

Answer 30

Yup. though did you understand why it is so?

Answer 31

no

Answer 32

oh so the answer to this problem is 2214cm/s because shamim converted meters to cm? xD

Answer 33

ya i converted it frm m to cm

Answer 34

so the speed in which the car is traveling at the top of the second hill is 22.14m/s or 2214cm/s?

Answer 35

lol I guess you knew. I believe you understood why v is calculated that way?

Answer 36

anyway i can solve this problem in my way too as i started b4

Answer 37

so the answer to this problem is 22.14m/s or 2214cm/s?

Answer 38

ya

Answer 39

ok ty :)

Answer 40

ok i m going to start

Answer 41

1st i wanna tell abt 1st pick

Answer 42

yup.
There will be a complication if we simply use the motion formula \(v^2 =u^2 +2aS\) though, since this question require a scalar answer, your answer might be a little off since it's a vector eq instead...you can try though.

Answer 43

u know the velocity of roller coaster on 1st pick is 0

Answer 44

sii C:

Answer 45

that means yes xD

Answer 46

lol @lilfayfay you french?

Answer 47

no, i take Spanish thats why :D

Answer 48

we can use this equation for scalar too

Answer 49

okie dokie :)))

Answer 50

oh right. I just checked. same answer. lol I guess i'm too careful.

Answer 51

so let the final velocity of roller coaster after coming from 1st pick to the ground=v

Answer 52

\[v ^{2}=u ^{2}+2gh\]

Answer 53

since u=0

Answer 54

did u understand why u=0?

Answer 55

because velocity is 0

Answer 56

\[or, v ^{2}=0^{2}+2 \times 10 \times 55\]

Answer 57

so why is u=0?

Answer 58

\[or, v=\sqrt{2 \times 10 \times 55}=33m\]

Answer 59

u=o, because the roller coaster was at rest when it was on 1st pick

Answer 60

rest means velocity is 0

Answer 61

ok i thought v=22.14m/s

Answer 62

not now

Answer 63

we hv to do more math to get result

Answer 64

now i wanna do math for pick 2

Answer 65

initial velocity u=33m/s

Answer 66

but Shadowys did an easier way?

Answer 67

final velocity of roller coaster when it is on the 2nd pick=v

Answer 68

ya his way is easier than mine

Answer 69

oh, ok :)

Answer 70

i think u should know all the ways to solve ur math. every way has some understanding

Answer 71

knowledge

Answer 72

should i proceed or not

Answer 73

proceed but im going to bed in a few mins since its late here lol

Answer 74

lol

Answer 75

i think u understood my way