For Exercises 120-121, consider 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 / sec 2 . A quarterback throws a football with an initial velocity of 62 ft/sec to a receiver 40 yd (120 ft) down the field. At what angle could the ball be released so that it hits the receiver's hands at the same height that it left the quarterback's hand? Round to the nearest tenth of a degree.
For Exercises 120-121, consider 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 / sec 2 . A quarterback throws a football with an initial velocity of 62 ft/sec to a receiver 40 yd (120 ft) down the field. At what angle could the ball be released so that it hits the receiver's hands at the same height that it left the quarterback's hand? Round to the nearest tenth of a degree.
Solution Summary: The author calculates the angle at which the ball is to be released so that it hits the receiver's hands at the same height as it left the quarterback’s hand.
For Exercises 120-121, consider 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
/
sec
2
.
A quarterback throws a football with an initial velocity of 62 ft/sec to a receiver 40 yd (120 ft) down the field. At what angle could the ball be released so that it hits the receiver's hands at the same height that it left the quarterback's hand? Round to the nearest tenth of a degree.
An article explains that the locomotion of different-sized animals can be compared when they have the same Froude number, defined as F =
gl
where v is the animal's velocity, g is the acceleration due to gravity
(9.81 m/sec2) and I is the animal's leg length.
(a) Different animals change from a trot to a gallop at the same Froude number, roughly 2.56. Find the velocity at which this change occurs for an animal with a leg length of 0.02 m.
(b) Ancient footprints of a dinosaur are roughly 0.9 m in diameter, corresponding to a leg length of roughly 3.6 m. By comparing the stride divided by the leg length with that of various modern creatures, it can be
determined that the Froude number for this dinosaur is roughly 0.025. How fast was the dinosaur traveling?
A billiard ball is dropped from a height of 144 feet. Use the position
function s (t) = -16t2 + vot + so to answer the following making
sure to put correct units of measurement.
a) Determine the position function s (t), the velocity function v (t),
and the acceleration function a (t).
b) When will the ball hit the ground? Put units of measurement.
c) What is the velocity of the ball at impact?
d) What is the acceleration of the ball at impact.
Type in your answer for each part into the text box below. If the
equation editor is needed, click on the V on the tool bar to access
it. Show all of your work on your paper.
DELL
F3
A researcher is nuning a simulation of an upward rocket to study the upward velocity of the
rocket using various fuel consumption rates. The researcher has found that the upward velocity
of the rocket can be represented by the following equation,
mo
v = u In
gt
Amo-qt.
where v=upward velocity of the rocket (m/s), u= the velocity at which fuel is expelled relative
to the rocket (m/s), m, = the initial mass of the rocket (kg), q = the fuel consumption rate
(kg/s), g = the downward accelemation of gravity (m/s), and t = time taken by the rocket for
the whole motion (s). If u = 1,500 m/s, m, = 125,000 kg, q = 2,300 kg/s and g= 9.81 m/s are
the values used by the researcher in one of his simulations, estimate the time, t at which v =
680 m/s using False Position method. It is known that the time, t is somewhere between 15 s
and 35 s. Perform THREE (3) iterations only and calculate the approximate percent relative
error, Ea| for every iteration.
University Calculus: Early Transcendentals (3rd Edition)
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