From a platform 35 meters above the ground, a ball is thrown

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ptsoccerboy

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From a platform 35 meters above the ground, a ball is thrown upward with an initial speed of 30 m/s. The approximate height of the ball above the ground t seconds later is given h(t) = 35 + 30t - 5t^2

a. After how many seconds does the ball hit the ground?

h(t) = 35 + 30t - 5t^2
5t^2 - 30t - 35 = 0
t^2 - 6t -7 = 0
(t-7)(t+1) = 0
t = 7 seconds

b. What is the domain of h?
Domain: All real numbers

c. What is the range of h?
Range : y (greater or equal) -80

d. After how many seconds does the ball reach its maximum height above the ground?

t = - (b/2a)
t = - (-30/10)
t = 3 seconds

Is my work valid and correct??
 
Re: From a platform 35 meters above the ground, a ball is th

ptsoccerboy said:
From a platform 35 meters above the ground, a ball is thrown upward with an initial speed of 30 m/s. The approximate height of the ball above the ground t seconds later is given h(t) = 35 + 30t - 5t^2

a. After how many seconds does the ball hit the ground?

h(t) = 35 + 30t - 5t^2
5t^2 - 30t - 35 = 0
t^2 - 6t -7 = 0
(t-7)(t+1) = 0
t = 7 seconds........... Correct

b. What is the domain of h?really - then why didn't you consider t= -1
Domain: All real numbers

c. What is the range of h?
Range : y (greater or equal) -80 - where did 'y' come from?

d. After how many seconds does the ball reach its maximum height above the ground?

t = - (b/2a)
t = - (-30/10)
t = 3 seconds........... Correct

Is my work valid and correct??
Click to expand...
 
Thank you!
oh, for b. i graphed it and it was all real numbers but what you said makes sense because it can't be all real numbers since time isn't negative.
and the 'y' is the y coordinate on the graph.
 
domain ...

\(\displaystyle \L 0 \leq t \leq 7\)

range ...

\(\displaystyle \L 0 \leq h \leq 80\)
 
what is the highest height of the ball?

what is the lowest height of the ball? (what would a negative value of h mean in the context of this problem?)
 
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