midterm_examA_F06_solutions

midterm_examA_F06_solutions - Physics 40A - Midterm Exam...

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Physics 40A - Midterm Exam Solutions - Fall 2006 - Exam A Problem 1 [25 points] A stone is thrown from the top of a building upward at an angle of 30° to the horizontal and with an initial speed of 20 m/s. (a) What are the horizontal and vertical components of the initial velocity? If the height of the building is 45 m, (b) how long is the ball in flight before it hits the ground? and (c) what are the components of the velocity of the stone just before it hits the ground? Solution: This is a projectile motion problem so the horizontal acceleration is zero and the vertical acceleration is g . We define the origin of our coordinate system at the initial position of the stone with + y vertically upward and + x horizontal (away from the building). (a) The x and y components of the initial velocity are v 0x = v 0 cos 0 = 20 m/s  cos30 ° = 17.3 m/s v 0y = v 0 sin 0 = 20 m/s  sin 30 ° = 10.0 m/s (b) The stone hits the ground when y = -45 m. To find the time we can use y ­ y 0 = v 0y t ­ ½ gt 2 . The initial height of the stone is y 0 = 0, so we obtain ­ 45 m ­ 0 = 10 m/s t ­ 1 2 9.8 m/s 2 t 2 or 4.9 m/s 2 t 2 ­ 10 m/s t ­ 45 m = 0 The roots of this quadratic equation are t = 10 ±  10 2 ­ 4 4.9 ­ 45 2 4.9 = 4.22 s and ­ 2.18 s The negative root is not physical, so we must have
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midterm_examA_F06_solutions - Physics 40A - Midterm Exam...

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