Question

1. If a rock is thrown vertically upward from the surface of Mars with velocity 15 m/s, its height after t seconds is h = 15t-1.86t^2


a. What is the velocity of the rock after 2s?

b. What is the velocity of the rock when its height is 25m on its way up? On its way down?

Answer 1

v = dh/dt

so can you differentiate 'h' w.r.t 't' ?

Answer 2

bdw, v = velocity

Answer 3

oh okay, sorry for the late reply :)

Answer 4

no problem :)

Answer 5

so what u got as v ?

Answer 6

i'm trying to solve it :)

Answer 7

okk, you'll need this formula \((x^n)' = n x^{n-1}\)

Answer 8

okay, sorry if it take me too long, i kinda forgot about solving this :(

Answer 9

hey, no problem, take your time :)
tell me if you find it difficult, i will try to explain it :)

Answer 10

ok, so i got \[\frac{ d(h) }{ d(t) }= 15-3.72t\]

Answer 11

yes! thats your equation for velocity!

v = 1.5 -3.72t

for part a) you need v at time t = 2
so, just plug in t = 2 in that equation! :)

Answer 12

ohh :)

Answer 13

so, its 7.56 m/s? :)

Answer 14

v(2) = 1.5 - 3.72(2) = ... ?
its not 7.56

Answer 15

oh no, sorry, 11.16 :)

Answer 16

i pressed the wrong button on my sci cal sorry

Answer 17

oh no, wait ... i thought its 15? and not 1.5? :O

Answer 18

no, my error :P
its 15 not 1.5
7.56 was correct! sorry

Answer 19

haha okay thankyou :)

Answer 20

now for part b
h = 25 is given,

so from
15t-1.86t^2 = 25

can you find 2 values of 't' ?
itsa quadratic in t

Answer 21

ohh okay, i'll try :)

Answer 22

uhm, can i ask? why was it equated to 25? i get it that it's the height and all but why was it 25? it thought its d(h)/d(t)? :)

Answer 23

"its height is 25m"
so h= 25 is given
and the only equation you have a "h" is
h = 15t-1.86t^2
so we need to use it to find the 't'

Answer 24

ohh, i get it now :)

Answer 25

okay, so i got x1=5.71 and x2=2.35 :)

Answer 26

yes, those are correct,
now you need the velocity at those times.

Answer 27

when the rock is 25m height on its way up, it took 2.35 seconds

so to get the velocity when its at height 25 on its way up, you will put t= 2.35 in the equation of velocity.

Answer 28

when the rock is 25m height on its way down, it took 5.71 seconds

so to get the velocity when its at height 25 on its way down, you will put t= 5.71 in the equation of velocity

Answer 29

the v = d/t formula right?

Answer 30

yes,the equation you got for velocity

v = 15-3.72 t

Answer 31

okay, so how do you know that 2.35 is for its way up and the other for its way down? :)

Answer 32

that is logic, since the rock is "thrown vertically up" it will reach the height of 25 m on its way up first, (so 2.35 sec )
then it still goes further up and at one point it will stop, then it will start coming down due to gravity and will again reach the height of 25m on its way down.
since coming down took more time, we take 5.71 as t for its way down

Answer 33

oh haha, thanks :)

Answer 34

ok so I got 6.258 m/s for 2.35s, and -6.2412 m/s for 5.71s :)

Answer 35

both are absolutely correct! :)

Answer 36

yay :)

so it kinda shows now in the answers, if it goes up, it has positive velocity and when it goes down, it has negative velocity. haha

Answer 37

yes! correct lol , thats what we got too :)

Answer 38

thankyou :)

can i as like 3 more questions? haha
its all word problems and i find them difficult esp. when they're on derivatives :(