Question

An object is launched upward from a platform so that its height
(in feet) above the ground *t* seconds after it is launched
is given by the function *h(t)*=-16*t*^2
+160*t+*176.

a. When does the object reach its maximum height? What is the maximum height?

b. When does the object hit the ground?

c. What is the *domain* and *range* of this
function (given the context)?

d. Sketch an accurate graph of this function *in an
appropriate window*. Mark on your graph the information from
parts a and b.

Answer #1

1. A projectile is launched upward at an angle so that its
distance (in feet) above the ground after ? seconds is given by the
function
?(?) = −20?2 + 105? Round each
answer to the nearest hundredth. a. When (i.e., how many seconds
after launch) will the projectile reach its maximum height?
_______________
b. How many seconds after launch will it take for the projectile to
return to earth?
_______________
c. What is the maximum height achieved by...

If an object is propelled upward from a height of s feet at an
initial velocity of v feet per second, then its height h after t
seconds is given by the equation h=−16t^2+vt+s, where h is in feet.
If the object is propelled from a height of 1212 feet with an
initial velocity of 9696 feet per second, its height h is given by
the equation h =minus−16t^2+96 +12. After how many seconds is the
height 120 feet?

An object is thrown vertically upward from a platform 80 feet
above the ground with a velocity of 64 feet per second. Given the
fact that the acceleration due to gravity is approximately -32
ft/sec/sec,
a) use antidifferentiation to determine the ‘velocity’, v(t), and
‘position above the ground’, s(t), functions; use these functions
to determine: b) when the object reaches its highest point; c) what
the highest point above the ground is; d) when it hits the ground;
e) the...

A flare is launched upward with an initial velocity of 80 ft/sec
from a height of 224 ft. Its height in feet
after t seconds is given by h t t t ( ) = − + + 16 80 224. 2 How
long will it take the flare to reach the ground?

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
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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?

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.

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...

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?

If a ball is thrown upward with a velocity of 64 ft/sec, then
its height after t seconds is s=64t-16t^2. When does the ball reach
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