qz2sol_3885f10 - least speed the ball will have during its...

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TA: Tomoyuki Nakayama Monday, September 13, 2010 PHY 2048: Physic 1, Discussion Section 3885 Quiz 2 (Homework Set #3) Name: UFID: Formula sheets are not allowed. Calculators are allowed. Do not store equations in your calculator. You need to show all of your work for full credit. ________________________________________________________________________________ A ball is to be shot from level ground with a certain speed. The figure below shows the range R it will have versus the launch angle θ 0 . a) What is the launch speed? According to the graph, the maximum range is 300 m. The maximum range is achieved when the projection angle is 45º. The equation for horizontal range yields R max = v 0 2 /g v 0 = (R max g) = 54.2 m/s b) The value of θ 0 determines the flight time; let t max represent the maximum flight time. What is the
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Unformatted text preview: least speed the ball will have during its flight if is chosen such that the flight time is 0.800 t max ? When the ball comes back to the ground level, the vertical displacement is zero. The flight time is 0 = v sin t-(1/2)gt 2 t = 2v sin /g Since the sine function takes its maximum value (= 1) when is 90. Thus the maximum flight time is t max = 2v /g Since we have to choose the projectile angle so that t = 0.8t max , the angle is 2v sin /g = 0.8(2v /g) sin = 0.8 = 53.1 The speed of the ball is minimum at the peak of the projectile motion, where y component of the velocity is zero. Therefore, the least speed is v min = v 0x = v cos = 32.5 m/s...
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This note was uploaded on 01/25/2011 for the course PHY 2048 taught by Professor Field during the Summer '08 term at University of Florida.

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