Finding velocity

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CoreyyV

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Sep 27, 2020
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the question is:

You shoot an arrow in the air. It falls to earth. Its height (in feet) after t seconds is h(t)=80t−16t^2. What is its velocity as it hits the ground? (Your answer should be negative since the arrow is going down.)

I know the first step is to find the derivative, which is: h'(t) = -32t + 80. I thought that next I was supposed to set the function equal to "0" and solve for "t", but when I do this, I end up with t=2.5, but when I answer it this way (or negative) it's incorrect.
 
CoreyyV said:
the question is:

You shoot an arrow in the air. It falls to earth. Its height (in feet) after t seconds is h(t)=80t−16t^2. What is its velocity as it hits the ground? (Your answer should be negative since the arrow is going down.)

I know the first step is to find the derivative, which is: h'(t) = -32t + 80. I thought that next I was supposed to set the function equal to "0" and solve for "t", but when I do this, I end up with t=2.5, but when I answer it this way (or negative) it's incorrect.
Click to expand...
You should set h(t) = 0 [NOT h'(t)] then you'll get t=5 and all will be well.
 
h'(t) is the velocity of the arrow. Now if you believe that the velocity will be equal to 0 just as the arrow hits the ground then you should set h'(t) = 0. But in my experience of throwing a ball in the air and having it fall into my hands I always observed that the ball starts off going up quickly, tyhen it immediately starts slowing down, then when the velocity slows down to 0 the ball starts coming down faster and faster. Now I know that a ball will not hit the ground (or my hands) with velocity = 0. Who knows, maybe an arrow is different? What do you think?

Armed with the velocity formula (h'(t)) you can find the velocity of the ball at any time t. If we only knew the time when the ball will hit the ground I would be in a great position to answer the question. How can I find the time when the height of the ball is 0? Hmm, what information does h(t) give me?
 
Jomo said:
h'(t) is the velocity of the arrow. Now if you believe that the velocity will be equal to 0 just as the arrow hits the ground then you should set h'(t) = 0. But in my experience of throwing a ball in the air and having it fall into my hands I always observed that the ball starts off going up quickly, tyhen it immediately starts slowing down, then when the velocity slows down to 0 the ball starts coming down faster and faster. Now I know that a ball will not hit the ground (or my hands) with velocity = 0. Who knows, maybe an arrow is different? What do you think?

Armed with the velocity formula (h'(t)) you can find the velocity of the ball at any time t. If we only knew the time when the ball will hit the ground I would be in a great position to answer the question. How can I find the time when the height of the ball is 0? Hmm, what information does h(t) give me?
Click to expand...
I think I get it now! We set h(t) to 0 because we already know the height, but are looking for the time when the height is 0
Subhotosh Khan said:
I hope you understand why we need to set h(t) = 0 !
Click to expand...
Yes I do, thanks!
 
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