having problems with word problems

[luiz_322]

i am really having problems with word problems can anybody help me please?

an object is thrown upward.the height of the object after thrown can be modeled by the equation h=-5t^2+35t , where h is the height above the ground in meters and t is the time in seconds.

and then it says at what time or times would the object be located at 60 meters above the ground?

thank you

 

[tkhunny]

h=-5t^2+35t
h is the height above the ground in meters.
t is the time in seconds.
At what time or times would the object be located at 60 meters above the ground?

Please read the definitions and think about how you would determine that.

t is the time in seconds.
At what time or times...?

h is the height above the ground in meters.
...located at 60 meters above the ground?

 

[soroban]

Hello, luiz_322!

You must learn to "read" these problems.
And don't let them intimidate you . . . they are mostly common sense.

An object is thrown upward.the height of the object after thrown
can be modeled by the equation: \(\displaystyle h\:=\:-5t^2\,+\,35t\),
where \(\displaystyle h\) is the height above the ground in meters and \(\displaystyle t\) is the time in seconds.

At what time or times would the object be located at 60 meters above the ground?

We are given a "height formula": \(\displaystyle \,h\:=\:-5t^2\,+\,35t\)

The question is: When is \(\displaystyle \,h\,=\,60\.?\)


Well, let's find out . . . Set \(\displaystyle h\) equal to 60: \(\displaystyle \,-5t^2\,+\,35t\:=\:60\)

Solve for \(\displaystyle t:\;\;5t^2\,-\,35t\,+\,60\:=\:0\)

We have: \(\displaystyle \;\;5(t^2\,-\,7t\,+\,12)\:=\:0\)

Factor: \(\displaystyle \;5(t\,-\,3)(t\,-\,4)\:=\:0\)

And we get: \(\displaystyle \,t\,=\,3\) and \(\displaystyle t\,=\,4\)

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Check

When \(\displaystyle t\,=\,3:\;\;h\;=\;-5\cdot3^2\,+\,35\cdot3\;=\;-45\,+\,105\;=\;60\)

When \(\displaystyle t\,=\,4:\;h\;=\;-5\cdot4^2\,+\,35\cdot4\;=\;-80\,+\,140\;=\;60\)

. . . See?

 

[luiz_322]

thank you so much that really helped

 

[tkhunny]

Sure, you now have the answer to THIS problem. Did you learn how to think about such things and solve other related problems? Did you learn to rely on your own brain? The pattern demonstrated here is not very encouraging. Sometimes is works OK.