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A projectile is launched at an angle of θ with a speed v0 at time t = 0s. At this same time a hoop with radius R = 0.5 m hanging on a ceiling a distance H above the projectile, and ∆x to the right of the projectile, is dropped from rest. In this problem assume the positive y-direction is upwards, and the positive x-direction is to the right. (Diagram attached in image) A) What is the minimum launch speed of the projectile, v0,m, such that it just makes it to the plane the hoop is contained in, ∆x away from the projectile’s initial position? Give your answer in terms of the variables given.   B) Assuming the projectile’s speed is greater than the v0,m you calculated above, at what angle must you launch the projectile such that it goes through the center of the falling hoop?   C) A wind now blows causing nonzero acceleration in the x-direction ax = 1 m/s^2 for the projectile, and a′x = 0.5 m/s^2 for the hoop. If θ = 30◦, v0 = 10 m/s, and H = 5m, how far to the right of the projectile must the hoop be placed on the ceiling such that the projectile will travel through the center of the hoop?

A projectile is launched at an angle of θ with a speed v0 at time t = 0s. At this same time a hoop with radius R = 0.5 m hanging on a ceiling a distance H above the projectile, and ∆x to the right of the projectile, is dropped from rest. In this problem assume the positive y-direction is upwards, and the positive x-direction is to the right. (Diagram attached in image) A) What is the minimum launch speed of the projectile, v0,m, such that it just makes it to the plane the hoop is contained in, ∆x away from the projectile’s initial position? Give your answer in terms of the variables given.   B) Assuming the projectile’s speed is greater than the v0,m you calculated above, at what angle must you launch the projectile such that it goes through the center of the falling hoop?   C) A wind now blows causing nonzero acceleration in the x-direction ax = 1 m/s^2 for the projectile, and a′x = 0.5 m/s^2 for the hoop. If θ = 30◦, v0 = 10 m/s, and H = 5m, how far to the right of the projectile must the hoop be placed on the ceiling such that the projectile will travel through the center of the hoop?

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A projectile is launched at an angle of θ with a speed v0 at time t = 0s. At this same time
a hoop with radius R = 0.5 m hanging on a ceiling a distance H above the projectile, and ∆x to the
right of the projectile, is dropped from rest. In this problem assume the positive y-direction is upwards,
and the positive x-direction is to the right. (Diagram attached in image)

A) What is the minimum launch speed of the projectile, v0,m, such that it just makes it to
the plane the hoop is contained in, ∆x away from the projectile’s initial position? Give your answer in
terms of the variables given.

 

B) Assuming the projectile’s speed is greater than the v0,m you calculated above, at what
angle must you launch the projectile such that it goes through the center of the falling hoop?

 

C) A wind now blows causing nonzero acceleration in the x-direction ax = 1 m/s^2 for the
projectile, and a′x = 0.5 m/s^2 for the hoop. If θ = 30◦, v0 = 10 m/s, and H = 5m, how far to the right
of the projectile must the hoop be placed on the ceiling such that the projectile will travel through the
center of the hoop?

 

 

A projectile is launched at an angle of with a speed vo at time t = 0s. At this same time a hoop with radius R = 0.5 m hanging on a ceiling a distance II above the projectile, and Ax to the right of the projectile, is dropped from rest. In this problem assume the positive y-direction is upwards, and the positive x-direction is to the right. O H 8 Ax Figure 1: Diagram of the problem. What is the minimum launch speed of the projectile, vo,m, such that it just makes it to the plane the hoop is contained in, Ar away from the projectile's initial position? Give your answer in terms of the variables given. Assuming the projectile's speed is greater than the vom you calculated above, at what angle must you launch the projectile such that it goes through the center of the falling hoop? A wind now blows causing nonzero acceleration in the x-direction a = 1 m/s² for the projectile, and a = 0.5 m/s² for the hoop. If = 30°, vo= 10 m/s, and H= 5m, how far to the right of the projectile must the hoop be placed on the ceiling such that the projectile will travel through the center of the hoop?
Transcribed Image Text:A projectile is launched at an angle of with a speed vo at time t = 0s. At this same time a hoop with radius R = 0.5 m hanging on a ceiling a distance II above the projectile, and Ax to the right of the projectile, is dropped from rest. In this problem assume the positive y-direction is upwards, and the positive x-direction is to the right. O H 8 Ax Figure 1: Diagram of the problem. What is the minimum launch speed of the projectile, vo,m, such that it just makes it to the plane the hoop is contained in, Ar away from the projectile's initial position? Give your answer in terms of the variables given. Assuming the projectile's speed is greater than the vom you calculated above, at what angle must you launch the projectile such that it goes through the center of the falling hoop? A wind now blows causing nonzero acceleration in the x-direction a = 1 m/s² for the projectile, and a = 0.5 m/s² for the hoop. If = 30°, vo= 10 m/s, and H= 5m, how far to the right of the projectile must the hoop be placed on the ceiling such that the projectile will travel through the center of the hoop?
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