For a projectile launched from ground level at an angle of elevation θ with an initial velocity v 0 , the maximum horizontal range is given by x max = v 0 2 sin 2 θ g , where g is the acceleration due to gravity g = 32 f t / sec 2 or g = 9.8 m / s e c 2 . If a toy rocket is launched from the ground with an initial velocity of 50 f t / sec and lands 73 ft from the launch point, find the angle of elevation of the rocket at launch. Round to the nearest tenth of a degree.
For a projectile launched from ground level at an angle of elevation θ with an initial velocity v 0 , the maximum horizontal range is given by x max = v 0 2 sin 2 θ g , where g is the acceleration due to gravity g = 32 f t / sec 2 or g = 9.8 m / s e c 2 . If a toy rocket is launched from the ground with an initial velocity of 50 f t / sec and lands 73 ft from the launch point, find the angle of elevation of the rocket at launch. Round to the nearest tenth of a degree.
Solution Summary: The author calculates the angle of elevation of the rocket if a toy rocket is launched from the ground with an initial velocity of 50ft/sec and lands at theta
For a projectile launched from ground level at an angle of elevation
θ
with an initial velocity
v
0
,the maximum horizontal range is given by
x
max
=
v
0
2
sin
2
θ
g
, where
g
is the acceleration due to gravity
g
=
32
f
t
/
sec
2
or
g
=
9.8
m
/
s
e
c
2
. If a toy rocket is launched from the ground with an initial velocity of
50
f
t
/
sec
and lands 73 ft from the launch point, find the angle of elevation of the rocket at launch. Round to the nearest tenth of a degree.
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
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