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A particle of mass m is moving along the +x-axis with constant speed vo. At time t = 0 it enters a region between two plates which are separated by a distance h and lie in the x - z plane as shown in the figure. The figure is a side view of the plates with the +z axis pointing out of the screen. After entering the region between the plates, the particle is acted on by both gravity (which points in the -y direction and has magnitude g) and by a time varying force that points upward, in the +y direction, with magnitude F = bt, where b is a positive constant and is large enough that the particle does not touch the bottom plate. 1. Sketch the trajectory of the particle. 2. How long does it take for the particle to reach its lowest point? 3. If the particle is initially at the midpoint between the two plates, what is the minimum possible value of b such that the particle does not hit the lower plate?

A particle of mass m is moving along the +x-axis with constant speed vo. At time t = 0 it enters a region between two plates which are separated by a distance h and lie in the x - z plane as shown in the figure. The figure is a side view of the plates with the +z axis pointing out of the screen. After entering the region between the plates, the particle is acted on by both gravity (which points in the -y direction and has magnitude g) and by a time varying force that points upward, in the +y direction, with magnitude F = bt, where b is a positive constant and is large enough that the particle does not touch the bottom plate. 1. Sketch the trajectory of the particle. 2. How long does it take for the particle to reach its lowest point? 3. If the particle is initially at the midpoint between the two plates, what is the minimum possible value of b such that the particle does not hit the lower plate?

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V h | "1470-24 g plates A particle of mass m is moving along the +x-axis with constant speed vo. At time t = 0 it enters a region between two plates which are separated by a distance h and lie in the x - z plane as shown in the figure. The figure is a side view of the plates with the +z axis pointing out of the screen. After entering the region between the plates, the particle is acted on by both gravity (which points in the -y direction and has magnitude g) and by a time varying force that points upward, in the +y direction, with magnitude F = bt, where b is a positive constant and is large enough that the particle does not touch the bottom plate. 1. Sketch the trajectory of the particle. 2. How long does it take for the particle to reach its lowest point? 3. If the particle is initially at the midpoint between the two plates, what is the minimum possible value of b such that the particle does not hit the lower plate? 4
Transcribed Image Text:V h | "1470-24 g plates A particle of mass m is moving along the +x-axis with constant speed vo. At time t = 0 it enters a region between two plates which are separated by a distance h and lie in the x - z plane as shown in the figure. The figure is a side view of the plates with the +z axis pointing out of the screen. After entering the region between the plates, the particle is acted on by both gravity (which points in the -y direction and has magnitude g) and by a time varying force that points upward, in the +y direction, with magnitude F = bt, where b is a positive constant and is large enough that the particle does not touch the bottom plate. 1. Sketch the trajectory of the particle. 2. How long does it take for the particle to reach its lowest point? 3. If the particle is initially at the midpoint between the two plates, what is the minimum possible value of b such that the particle does not hit the lower plate? 4
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