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.
A sky diver weighing 192 lb (including equipment) falls vertically downward from a very high altitude. Assume that the air resistance is proportional to the falling velocity with the constant k = 0.6, the acceleration due to gravity g = 32ft/sec2, and that the positive direction is downward.
What is the terminal velocity of the sky diver if he/she never opens the parachute?
a quarterback throws a football with an initial velocity of 72 ft/sec at an angle of 25. the height of a ball can be modeled by h(t) = -6t^2 + 30.4t +5 where h(t) is the height (in ft) and t is the time seconds after release.
a, Determine the time at which the ball will be at its maximum height.
b, Determine the maximum height of the ball.
c, Determine the amount of time required for the ball to reach the reciver's hands if the receiver catches the ball at a point 3 ft off the ground.
A body is thrown at an angle α with the horizontal. Neglecting air resistance, determine the angle α, at which the horizontal range is maximum.
University Calculus: Early Transcendentals (3rd Edition)
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