Suppose an arrow is shot upward on a certain planet with an intial height of 1.7 meters and an initial velocity of 70 m/s. Then its height in meters after t seconds is given by h(t)=70t−7.9t2+1.7 A) First, graph the function h(t) with Desmos (with an appropriate window for the situation - not too big and not too small) and print it out or make a hand-drawn and NEAT graph of the function h(t). Make sure there is a numerical scale on both axes. Next, draw the tangent line to the curve at t=5 seconds
Suppose an arrow is shot upward on a certain planet with an intial height of 1.7 meters and an initial velocity of 70 m/s. Then its height in meters after t seconds is given by
h(t)=70t−7.9t2+1.7
A) First, graph the function h(t) with Desmos (with an appropriate window for the situation - not too big and not too small) and print it out or make a hand-drawn and NEAT graph of the function h(t).
Make sure there is a numerical scale on both axes. Next, draw the tangent line to the curve at t=5 seconds. (Don't do any math please - really just draw it with your hand or use a line in an art program if you want to use a computer).
Then, choose two points on that tangent line that are far apart from each other, clearly label them on your graph, and find the slope of that tangent line that you drew.
What were your two points that you chose on the tangent line (that are clearly marked on your graph that you just uploaded)?
( , )
and
( , )
And the slope of the tangent line using those two points is:
m=
B) Now remember that the slope of the tangent line at a point is actually the velocity of the arrow at that point. Go ahead and use calculus to find the velocity of the arrow at t= 5 seconds.
The velocity of the arrow at t=5 seconds is(_ ) meters per second.
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