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The figure below shows a track with a small marble starting from rest at a height h, above the point where the marble leaves the track. When the marble leaves the track, it leaves at an angle e with the horizontal and at a height h, above the ground. It then flies through the air until it hits the ground at a distance D to the right from the bottom of the table. Starts on Track Here Leaves Track Here Lands on Ground Here D. A sample path taken by the marble

The figure below shows a track with a small marble starting from rest at a height h, above the point where the marble leaves the track. When the marble leaves the track, it leaves at an angle e with the horizontal and at a height h, above the ground. It then flies through the air until it hits the ground at a distance D to the right from the bottom of the table. Starts on Track Here Leaves Track Here Lands on Ground Here D. A sample path taken by the marble

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Problem #4 Undergraduate Dynamics Problem The figure below shows a track with a small marble starting from rest at a height h, above the point where the marble leaves the track. When the marble leaves the track, it leaves at an angle e with the horizontal and at a height h, above the ground. It then flies through the air until it hits the ground at a distance D to the right from the bottom of the table. Starts on Track Here Leaves Track Here Lands on Ground Here D A sample path taken by the marble Given the values of h,, h̟ and the launch angle e, а.) b.) determine an expression for D. Determine (in terms of y = h,lh,) the launch angle so that D is as large as possible. c.) Determine (in tems of h, and h) this largest value of D (callit Dmx). Compute these values using h, = 1.5 feet, h, = 3.0 feet and g = 32 feet/sec?. d.)
Transcribed Image Text:Problem #4 Undergraduate Dynamics Problem The figure below shows a track with a small marble starting from rest at a height h, above the point where the marble leaves the track. When the marble leaves the track, it leaves at an angle e with the horizontal and at a height h, above the ground. It then flies through the air until it hits the ground at a distance D to the right from the bottom of the table. Starts on Track Here Leaves Track Here Lands on Ground Here D A sample path taken by the marble Given the values of h,, h̟ and the launch angle e, а.) b.) determine an expression for D. Determine (in terms of y = h,lh,) the launch angle so that D is as large as possible. c.) Determine (in tems of h, and h) this largest value of D (callit Dmx). Compute these values using h, = 1.5 feet, h, = 3.0 feet and g = 32 feet/sec?. d.)
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