SOLUTION: Hello I really need some assistance with the following algebra word problem: "An Object is thrown upward from the top of a 160 foot building with an initial velocity of 48 feet

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: Hello I really need some assistance with the following algebra word problem: "An Object is thrown upward from the top of a 160 foot building with an initial velocity of 48 feet       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 348238: Hello I really need some assistance with the following algebra word problem:
"An Object is thrown upward from the top of a 160 foot building with an initial velocity of 48 feet per second. The height h of the object after t seconds is given by the quadractic equation h=16t^2 + 48t + 160. When will the object hit the ground?
Thank you for your assistance in advance
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You can use the equation to get clues for how to proceed
Like lots of motion problems, it starts at t+=+0
What is h at t+=+0?
+h=16t%5E2+%2B+48t+%2B+160
+h=16%2A0%5E2+%2B+48%2A0+%2B+160
h+=+160
This is saying that you are 160 ft above ground when you
throw the object up. There will be some value of t
that will give me h+=160 when the object is on it's way
down. This means it's back at your level on top of the building.
You want to find t at h+=+160+-+160 which is h+=+0
+h=+16t%5E2+%2B+48t+%2B+160
+0=+16t%5E2+%2B+48t+%2B+160
+0=+t%5E2+%2B+3t+%2B+10
I can solve using quadratic formula
t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+3
c+=+10
t+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A10+%29%29%2F%282%2A1%29+
t+=+%28-3+%2B-+sqrt%28+9+-+40+%29%29%2F2+
This makes no sense- the square root is of a negative
The equation should be
+h+=+-16%5E2+%2B+48t+%2B+160, then
+0+=+-t%5E2+%2B+3t+%2B+10
a+=+-1
b+=+3
c+=+10
t+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A%28-1%29%2A10+%29%29%2F%282%2A%28-1%29%29+
t+=+%28-3+%2B-+sqrt%28+9+%2B+40+%29%29%2F-2+
t+=+%28-3+%2B+7%29%2F-2 (can't use this - negative number)
t+=+%28-3+-7%29%2F-2
t+=+5
The object hits the ground in 5 sec
I can plot this as h vs t (note that h is divided by 16 here)
+graph%28+400%2C+400%2C+-1%2C+10%2C+-1%2C+13%2C+-x%5E2+%2B+3x+%2B+10%29+