Question

The formula for projectile motion is: h(t) = -16t2 + vot + so, where h is the height (at a given time t), vo is the initial velocity and so is the starting height.

A rocket is launched straight up from the top of an 64 foot building with the initial velocity of 160 feet per second. Find the time interval when the rockets' height exceeds 400 feet.

Answer 1

where are you stuck

Answer 2

how do i solve this??

Answer 3

we start by interpreting the question and figure out what stuff we're given, and what exactly we're asked to solve.

Answer 4

you can fill into your equation the values you are given. Ooops, I won't interfere with ganeshie8's lesson...I dislike very much when people do that to me! Good luck with this! You're in good hands...

Answer 5

read the question and can you tell me below :
1) what we're given ?
2) what we need to solve ?

Answer 6

given is the height of the building and the original velocity

Answer 7

thats right ! and what are we trying to solve ?

Answer 8

the time interval when the rockets' height exceeds 400 feet.

Answer 9

Excellent!!

so we're given below :
initial height, \(S_0 = 64 \) feet
initial velocity, \(V_0 = 160\) feet per second

and we need to find \(\large t\) at which the height equals \(400\) feet

Answer 10

plugin the values in the given equation for height

Answer 11

\[\large h(t) = -16t^2 + V_0 t + S_0,\]

Answer 12

t is 2.5?

Answer 13

\[\large 400 = -16t^2 + 160 t + 64\]

Answer 14

nope, try again.
we need to solve above quadratic ^

Answer 15

you minus 64 from both sides right

Answer 16

im thinking of dividing 16 both sides first

Answer 17

\[\large \dfrac{400}{16} = \dfrac{-16t^2 + 160 t + 64}{16}\]

Answer 18

25=160t+64

Answer 19

you need to divide each term on the right hand side cuz all are connected by addition..

Answer 20

\[\large 25 = -t^2 + 10 t + 4\]

Answer 21

send the right hand stuff to left :

\[\large t^2 - 10t +21 = 0\]

Answer 22

see if you can factor this quadratic

Answer 23

ok t= 7,3

Answer 24

Yes !! which one is small ? 7 or 3 ?

Answer 25

3

Answer 26

so that goes first 3 then 7

Answer 27

so, at t = 3 the rocket's height reaches 400 feet

Answer 28

ok it wants the interval notation so its (3,7)?

Answer 29

that looks good ^

Answer 30

ok good!!!

Answer 31

between t = 3 and t=7, the rocket's height stays above 400

Answer 32

ok cool

Answer 33

good job !!

Answer 34

thank you

Answer 35

ok how about something like this?

Answer 36

The equation for the calculation of the parallel resistance R1 and R2 is given by:
Rtotal = R1R2
R1 + R2
If the parallel circuit R2 = 4 ohms, find the interval in which Rtotal is at most 2 ohms.

Answer 37

R1R2 over R1+R2

Answer 38

\[\large R_{\text{total}} = \dfrac{R_1 R_2}{R_1 + R_2}\]

Answer 39

like that ?

Answer 40

yes

Answer 41

Alright, so what stuff are we given, and what we need to solve exactly ?

Answer 42

R2 = 4 ohms

Answer 43

R TOTAL is at the most 2 ohms

Answer 44

that means Rtotal cannot exceed 2ohms

Answer 45

yes

Answer 46

so it would either be [0, 4]

Answer 47

lets see

Answer 48

you would divide right?

Answer 49

whats that sign mean? after the 4?

Answer 50

wait a sec, actually you're correct ! i made a mistake... sorry :/

Answer 51

ok so its 0,4

Answer 52

\[\large 2 \ge \dfrac{4R_1 }{R_1 + 4} \]

\[\large 2R_1 + 8 \ge 4R_1 \]

\[\large R_1 \le 4 \]

Answer 53

\(\large [0, 4]\) is right !

Answer 54

ok cool thanks

Answer 55

can we do another?

Answer 56

Sue drove her car at 25 mph for the first part of the trip and then changed her speed to 75 mph for the second part. If the entire trip is 725 miles and took 13 hours, how many hours are traveled at each speed?

Answer 57

hey please post it as a new question...

Answer 58

ok

Answer 59

ty :) when possible, please limit to one question per thread :)

Answer 60

ok ty:)