Projectile Motion The position of a projectile fired with an nitial velocity va feet per second and at an angle 0 to the norizontal at the end of t seconds is given by the parametric quations x = (Vo cos 0)t y = (vo sin 0)t – 16r² See the illustration. R a) Obtain the rectangular equation of the trajectory, and identify the curve. b) Show that the projectile hits the ground (y = 0) when Vo sin 0. 16 c) How far has the projectile traveled (horizontally) when it strikes the ground? In other words, find the range R. d) Find the time t when x = y. Next find the horizontal distance x and the vertical distance y traveled by the projectile in this time. Then compute Vr? + y². This is the distance R, the range, that the projectile travels up a plane inclined at 45° to the horizontal (x = y). See the following illustration. (See also Problem 99 in Section 76.) 45
Projectile Motion The position of a projectile fired with an nitial velocity va feet per second and at an angle 0 to the norizontal at the end of t seconds is given by the parametric quations x = (Vo cos 0)t y = (vo sin 0)t – 16r² See the illustration. R a) Obtain the rectangular equation of the trajectory, and identify the curve. b) Show that the projectile hits the ground (y = 0) when Vo sin 0. 16 c) How far has the projectile traveled (horizontally) when it strikes the ground? In other words, find the range R. d) Find the time t when x = y. Next find the horizontal distance x and the vertical distance y traveled by the projectile in this time. Then compute Vr? + y². This is the distance R, the range, that the projectile travels up a plane inclined at 45° to the horizontal (x = y). See the following illustration. (See also Problem 99 in Section 76.) 45
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![Projectile Motion The position of a projectile fired with an
nitial velocity va feet per second and at an angle 0 to the
norizontal at the end of t seconds is given by the parametric
quations
x = (Vo cos 0)t y = (vo sin 0)t – 16r²
See the illustration.
R
a) Obtain the rectangular equation of the trajectory, and
identify the curve.
b) Show that the projectile hits the ground (y = 0) when
Vo sin 0.
16
c) How far has the projectile traveled (horizontally) when
it strikes the ground? In other words, find the range R.
d) Find the time t when x = y. Next find the horizontal
distance x and the vertical distance y traveled by the
projectile in this time. Then compute Vr? + y². This is
the distance R, the range, that the projectile travels up a
plane inclined at 45° to the horizontal (x = y). See the
following illustration. (See also Problem 99 in Section 76.)
45](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F487f4576-4fe6-403d-a282-ea98d5043816%2F4e7b5b9d-5748-4e61-be6e-f2d3cb78bdf0%2Fgo4u2f_processed.png&w=3840&q=75)
Transcribed Image Text:Projectile Motion The position of a projectile fired with an
nitial velocity va feet per second and at an angle 0 to the
norizontal at the end of t seconds is given by the parametric
quations
x = (Vo cos 0)t y = (vo sin 0)t – 16r²
See the illustration.
R
a) Obtain the rectangular equation of the trajectory, and
identify the curve.
b) Show that the projectile hits the ground (y = 0) when
Vo sin 0.
16
c) How far has the projectile traveled (horizontally) when
it strikes the ground? In other words, find the range R.
d) Find the time t when x = y. Next find the horizontal
distance x and the vertical distance y traveled by the
projectile in this time. Then compute Vr? + y². This is
the distance R, the range, that the projectile travels up a
plane inclined at 45° to the horizontal (x = y). See the
following illustration. (See also Problem 99 in Section 76.)
45
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