Free-Falling Object In Exercises 101 and 102. 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?
Free-Falling Object In Exercises 101 and 102. 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 explains how to calculate the velocity of a can of paint when it touches the ground.
In Exercises 101 and 102. 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?
Use the properties of logarithms, given that In(2) = 0.6931 and In(3) = 1.0986, to approximate the logarithm. Use a calculator to confirm your approximations. (Round your answers to four decimal places.)
(a) In(0.75)
(b) In(24)
(c) In(18)
1
(d) In
≈
2
72
Find the indefinite integral. (Remember the constant of integration.)
√tan(8x)
tan(8x) sec²(8x) dx
Find the indefinite integral by making a change of variables. (Remember the constant of integration.)
√(x+4)
4)√6-x dx
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