projectile motion

wingyue

2010-10-31 6:58 am

有條mc我唔明
Two fireworks, P and Q are projected from the same point on the ground at thw same time. P is projected vertically upwards at a speed of 30m-s while Q is projected at an angle of 30o to the horizontal at a speed of 60m-s.

Which of the following statements are correct?
(1) P and Q can reach the same height
(2) P and Q have the same acceleration throught their fight in the air.
(3) Pand Q are momentarily at rest at their highest points.

答案係(1) and (2)係correct
但我唔明點解(3)係incorrect?

更新1:

重有一題想問 A stone of mass 0.2kg is projected an angle of 60 to the horizontal with a speed of 2ms-1. what is the max potrntial energy gain by the stone?neglect air resistance 答案係0.3J

回答 (1)

天同

2010-10-31 7:41 am

✔ 最佳答案

At the highest point, P is momentarily at rest because it has just finished the upward journey and starts to fall down under gravity.

But Q has a constant horizontal speed of 60.cos(30) m/s = 52 m/s. At the highest point, there is no vertical speed, but there is an horizontal speed of 52 m/s which propels Q to move throughout the whole journey. Hence, Q is moving horizontally at the highest point and thus is not momentarily at rest.

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Consider the vertical motion of the stone.Use equation of motion: v^2 = u^2 + 2.a.swith v = 0 m/s (at highest point), u = 2.sin(60) m/s = 1.732 m/sa = -g(=-10 m/s2), s = ?hence, 0 = 1.732^2 + 2.(-10).si.e. s = 0.15 mPotential energy gained = 0.2g x 0.15 J = 0.3 J

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