(a) Use a graphing utility to generate the trajectory of a paper airplane whose equations of motion for t ≥ 0 are x = t − 2 sin t , y = 3 − 2 cos t (b) Assuming that the plane flies in a room in which the floor is at y = 0 , explain why the plane will not crash into the floor. [For simplicity, ignore the physical size of the plane by treating it as a particle.] (c) How high must the ceiling be to ensure that the plane does not touch or crash into it?
(a) Use a graphing utility to generate the trajectory of a paper airplane whose equations of motion for t ≥ 0 are x = t − 2 sin t , y = 3 − 2 cos t (b) Assuming that the plane flies in a room in which the floor is at y = 0 , explain why the plane will not crash into the floor. [For simplicity, ignore the physical size of the plane by treating it as a particle.] (c) How high must the ceiling be to ensure that the plane does not touch or crash into it?
(a) Use a graphing utility to generate the trajectory of a paper airplane whose equations of motion for
t
≥
0
are
x
=
t
−
2
sin
t
,
y
=
3
−
2
cos
t
(b) Assuming that the plane flies in a room in which the floor is at
y
=
0
,
explain why the plane will not crash into the floor. [For simplicity, ignore the physical size of the plane by treating it as a particle.]
(c) How high must the ceiling be to ensure that the plane does not touch or crash into it?
A golf ball is hit with an initial velocity of 135 feet per second (about 92 miles per hour) at an angle of 60
degrees to the horizontal. There is a 5 foot-per-second headwind that reduced the horizontal velocity by that
amount. The vertical component of velocity is unaffected.
Find parametric equations for the position of the ball relative to the tee as a function of time after it is hit.
I=
135 cos
60π
180
5
=(1
y=-16t² + 135 sin
60π
180
After how many seconds does the ball hit the ground?
t
seconds
How far does the ball travel before hitting the ground?
feet
Graph the parametric equations
(x(t) = sin t
(y(t) = sin 2t
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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