SOLUTION: Hello, I am having trouble answering two questions on projectiles using formulas: d=16t^2 where d=distance in feet that an object falls, in t seconds, regardless of weight. And, i
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Question 1087912: Hello, I am having trouble answering two questions on projectiles using formulas: d=16t^2 where d=distance in feet that an object falls, in t seconds, regardless of weight. And, if a projectile is launched upward from the ground with an initial velocity of 73.5 m per second, neglecting air resistance, it's height, in meters, above the ground t seconds after projection is given by the formula: d= -4.9t^2+73.5t.
*After how many seconds will the projectile be 100 m above the ground? I took 100 and divided by 73.5 and got 1.36 seconds?
*How long will it take for the projectile to return to the ground? I converted the 100 m to 328.084 ft and used d=16t^2 to get 4.53 seconds? Could someone please tell me if these are correct? If not, could you please help me figure this out? Any help would be most appreciated! Thanks!
Found 3 solutions by solver91311, ikleyn, josmiceli:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You want to know the value of t that makes 
, so solve the quadratic:
which you will probably want to rearrange into standard form, thus:
The smaller zero of the equation will be the time it reaches 100 meters on the way up and the larger solution will be the time it reaches 100 meters again on the way down.
The ground is 0 meters above the ground. The projectile is at 0 meters at time 0, and then again at the non-zero value of t that satisfies
John
My calculator said it, I believe it, that settles it
Answer by ikleyn(52765) (Show Source): You can put this solution on YOUR website!
.
In this site, there is a bunch of lessons on a projectile thrown/shot/launched vertically up
- Problem on a projectile moving vertically up and down
- Problem on an arrow shot vertically upward
- Problem on a ball thrown vertically up from the top of a tower
- Problem on a toy rocket launched vertically up from a tall platform
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this textbook under the topic "Projectiles launched/thrown and moving vertically up and dawn".
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
For the question:
" After how many seconds will the projectile be 100 m above the ground? "
the units are meters and seconds, so all you need is the formula
-----------------------------------------
The formula is a parabola with a peak, so unless the projectile is at its
peak at 100 m above ground, there will be 2 solutions, one when the projectile is
on the way up, and another on the way down.
------------------------------------------
m
Plug this value into the formula
Use the quadratic formula
sec
and, the other solution is:
sec
These are the 2 solutions
--------------------------------
" How long will it take for the projectile to return to the ground? "
At ground level,
This is when the projectile is launched
In 15 sec, the projectile hits the ground.
--------------------------------------
I can use this answer to check my 1st answer.
The peak will be at 1/2 this time, or sec
---------------------------------------------
My solutions for the height of m must be
equally spaced on either side of sec, so I can say:
Right on the money!
----------------------
Here is a plot of this problem:
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