Question

2) An object is thrown upward with an initial velocity of 144
feet per second from an initial height of 160 feet. Use the fact
that the acceleration due to gravity is -32 feet per second per
second to answer the following: a) Using integration, find the
position function giving the height s as a function of time t. b)
At what time will the ball reach maximum height? c) When does the
ball hit the ground? d) What is the maximum height of the ball? e)
At what velocity does the ball hit the ground?

3) Use 5 rectangles to approximate the area under the region lying
between the graph of ?(?) = ?3, the x-axis, x = 0 and x = 3 using
upper sums (circumscribed rectangles). Construct a picture of the
area you are finding.

4) Find the derivative of the following functions. Explain the
method you used to find the derivative: a) ?(?) = 4?9 − 7?5 − 3 ?4
+ 5? − 8

b) ℎ(?) =

7?4 ????

c) ℎ(?) = 6?2cos(2?3)

5) Find the equation of the tangent line to the graph of the
function ℎ(?) = 4?3 4?3−2 at ? = 1

6) A rancher wants to construct an area where he can keep his
horses. He has 1450 feet of fencing with which to enclose two
adjacent rectangular spaces which are separated by a fence. The
rectangular spaces are of equal sizes. What dimensions should be
used so that the enclosed area will be a maximum? (Hint: draw a
sketch of the area, making sure to account for the problem having 2
equally sized rectangles.)

Answer #1

11. a ball is thrown up from the ground with an initial velocity
of 120 feet per second. The height s in feet can be expressed as a
function of time t in seconds by s(t)=85t-16t^2 a. when does the
ball reach its maximum height b. what is the maximum height c. when
does the ball hit the ground
12. a farmer has 2800 feet of fencing material with which to
enclose a rectangle field that borders a straight stream....

Arnold hit a golf ball with an initial velocity of 150 feet per
second at an angle of 40° above the horizontal. What is the maximum
height reached by the golf ball?

A ball is thrown vertically upward from a height of 5 ft with an
initial velocity of 83 ft/s. The distance s (in feet) of the ball
from the ground after t seconds is s = s(t) = 5 + 83t − 16t^2. (a)
What is the velocity v, in feet per second, of the ball after 2
seconds?
(b) When, in seconds, will the ball reach its maximum height?
(Round your answer to one decimal place.)
(c) What is...

A
ball is thrown directly upward from a height of 3 ft with an
initial velocity of 20 ft/sec. the function s(t) = -16t^2+20t+3
gives the height of the ball, in feet, t seconds after it has been
thrown. Determine the time at which the ball reaches its maximum
height and find the maximum height.

17) A ball is thrown vertically upward from ground level with an
initial velocity of 96 feet per second. Use ?(?) = −32 ??⁄ 2.
a) How long will it take it to rise to its maximum height? b)
What is the maximum height?

You throw a tennis ball North with an initial speed of 24 feet
per second, at an angle of elevation 30° above horizontal,
releasing the ball 4 feet above the ground. A steady wind imparts a
constant acceleration of 3 feet per second squared Eastward.
Acceleration due to gravity is a constant 32 feet per second
squared downward.
Throughout the problem, let East be the positive x
direction, North the positive y direction, and up the
positive z direction. Let...

If a cannonball is shot directly upward with a velocity of 208
feet per second, its height above the ground after t seconds is
given by ?(?) = 216? − 16? 2 .
a. Find the velocity and acceleration after t seconds.
b. What is the maximum height the cannonball reaches?
c. How long does it take to reach the maximum height?

An object is thrown upward at a speed of 184 feet per second by a
machine from a height of 8 feet off the ground. The height hh of
the object after tt seconds can be found using the equation
h=−16t2+184t+8
When will the height be 528 feet?
When will the object reach the ground?

A ball is thrown directly upward from the edge of a
rock and travels such that after t seconds its height in feet above
the ground is given by the equation s(t) =-2.5t^2+10t+2
1.Find the equation that represents the instant
velocity v(t) of the ball on t time.
2.When does the ball has zero velocity?
3. What is the maximum height that the ball
reaches?
4. When does the ball touches the surface of the
Earth?
5. build the graph...

An object is thrown upward at a speed of 128 feet per second by
a machine from a height of 13 feet off the ground. The height (h)
of the object after (t) seconds can be found using the equation
h(t)=−16t2+128t+13
When will the height be 269 feet? and When will the object reach
the ground?

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