Please help!

[yankees1004]

"A ball is shot into the air from the edge ofa building, 50 ft. above the ground. It’sinitial velocity is 20 feet per second. Theequations h=-16t+20t+50 can be​

used to model the height of the ball after tseconds. About how long does it take the​

ball to hit the ground?"


Can anyone find the soultion to this word problem? I am having difficulty. I need for the work to be shown. I would appreciate it very much for anyone who helps.

 

[srmichael]

"A ball is shot into the air from the edge ofa building, 50 ft. above the ground. It’sinitial velocity is 20 feet per second. Theequations h=-16t+20t+50 can be​

used to model the height of the ball after tseconds. About how long does it take the​

ball to hit the ground?"


Can anyone find the soultion to this word problem? I am having difficulty. I need for the work to be shown. I would appreciate it very much for anyone who helps.

First, I believe you meant $\displaystyle h=-16t^2+20t+50$

Second, what have you tried? Hint: What does h equal when the ball hits the ground?

 

[yankees1004]

Ball is shot from the edge of building so its path must be parabolic.
For parabolic path a quadratic equation used to model the height of the ball.
Given equation h=-16t+20t+50 represents the linear equation.
I believe you meant h=-16t ²+20t+50
we want to find how long does it take the ball to hit the ground.
When ball hits the ground height h must be equal to zero
so above equation becomes
-16t ²+20t+50=0
multiplying both sides by -1 we get
16t ²-20t-50=0
Dividing both sides by 2
8t ²-10t-25=0 ....(1)
We use Factorization method to solve the above equation
(8t ²*-25=-400t ² so we can write -10t=-20t+10t as -20t*10t=-200t ²)
So (1) can be written in a form
8t ² -20t+10t-25=0
Taking common from first two and last two term
4t(2t-5)+5(2t-5)=0
Taking 2t-5 common
(2t-5)(4t+5)=0 (2t-5)=0 or (4t+5)=0
t=5/2 or t=-5/4 (neglect t=-5/4 as time is never negative)

Ball takes t=5/2=2.5 seconds to hit the ground.

I hope this solution makes you happy.

First, I believe you meant $\displaystyle h=-16t^2+20t+50$

Second, what have you tried? Hint: What does h equal when the ball hits the ground?

thank you so much! I really appreciate it. Oops sorry for the mistake