In Exercises 105 and 106, use the position function s ( t ) = − 16 t 2 + 500 , which gives the height (in feet) of an object that has fallen for t seconds from a height of 500 feet. The velocity at time t = a seconds is given by lim t → a s ( a ) − s ( t ) a − t ⋅ A construction worker drops a full paint can from a height of 500 feet. When will the paint can hit the ground? At what velocity will the paint can impact the ground?
In Exercises 105 and 106, use the position function s ( t ) = − 16 t 2 + 500 , which gives the height (in feet) of an object that has fallen for t seconds from a height of 500 feet. The velocity at time t = a seconds is given by lim t → a s ( a ) − s ( t ) a − t ⋅ A construction worker drops a full paint can from a height of 500 feet. When will the paint can hit the ground? At what velocity will the paint can impact the ground?
Solution Summary: The author calculates the Velocity of a paint can when it touches the ground.
In Exercises 105 and 106, use the position function
s
(
t
)
=
−
16
t
2
+
500
,
which gives the height (in feet) of an object that has fallen for t seconds from a height of 500 feet. The velocity at time
t
=
a
seconds is given by
lim
t
→
a
s
(
a
)
−
s
(
t
)
a
−
t
⋅
A construction worker drops a full paint can from a height of 500 feet. When will the paint can hit the ground? At what velocity will the paint can impact the ground?
During Ricardo noticed an ink stain with a diameter of about 3 cm on the front of his teacher’s shirt. He then noticed that there was a pen in the pocket and that the ink blot was continuing to spread across the front of the teacher’s shirt. He estimated that the diameter of the ink blot seemed to be growing by about 0.5 cm every 2 minutes.
a) Write an equation for the RADIUS, r, of the ink stain, as a function of time, t. Assume that t = 0 represents the time that Ricardo first noticed the ink stain.
b) Write an equation showing the AREA, A, of the ink stain as a function of the time t. (Hint: It might help to first write A as a function of r. )
c) Draw a graph of the function A(t) for 10 minutes.
d) At what time is the area of the ink stain about 25 square centimeter? Show how you answer this question. (i.e. ”I found it using desmos” is not sufficient)
The function p(t) = 20 sin 2xt + 100 models a person's blood pressure while resting, where p(1)
represents the blood pressure, in millimetres of mercury (mmHg), and t is the time, in seconds.
Determine minimum blood pressure, within the first second, and when it occurs.
Sketch the graph of the function f(x)=-x2 +4x-1. Find the equation of the line that is tangent to this graph at the point (2, 3).
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