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 . If a soccer ball is kicked from ground level with an initial velocity of 28 m/sec, what is the smallest positive angle at which the player should kick the ball to reach a teammate 48 m down the field? Assume that the ball reaches the teammate at ground level on the fly. 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 . If a soccer ball is kicked from ground level with an initial velocity of 28 m/sec, what is the smallest positive angle at which the player should kick the ball to reach a teammate 48 m down the field? Assume that the ball reaches the teammate at ground level on the fly. 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
.
If a soccer ball is kicked from ground level with an initial velocity of 28 m/sec, what is the smallest positive angle at which the player should kick the ball to reach a teammate 48 m down the field? Assume that the ball reaches the teammate at ground level on the fly. 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?
Differentiate the ff equation:
A racecar travels on the flat road and its motion is monitored.
i)
If the car is accelerating at 9 m/s² and the initial velocity of the car is 5 m/s,
what is the equation for the velocity of the car?
b)
ii)
iii)
Find the distance travelled by the car as a function of time?
Calculate the distance travelled by the car for the first 30 seconds.
University Calculus: Early Transcendentals (4th Edition)
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