5. The magnitude of a vector cannot be smaller than the magnitude of any of its components. TRUE FALSE

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1 Physics 1 Exam 2 Practice S14 Name: Show work for ANY credit. Box answers. Assume 3 significant figures! Ignore air resistance. NEATNESS COUNTS. Conceptual Questions. (2 points each) 1. A 100 g ball rolls off a table and lands 2.0 m from the base of the table. A 200 g ball rolls off the same table with the same speed. It lands at distance a. 1.0 m. b. Between 1 m and 2 m. c. 2.0 m. d. Between 2 m and 4 m. e. 4.0 m. 2. To achieve maximum range of a projectile, on Earth we must launch it at 45. On the moon we should launch it at: A. greater than 45. B. less than 45. C Projectiles 1 and 2 are launched over level ground with the same speed but at different angles. Which hits the ground first? Ignore air resistance. A. Projectile 1 hits first. B. Projectile 2 hits first. C. They hit at the same time. D. There s not enough information to tell. 4. A cannon shoots a ball and at the same time an identical ball is dropped from rest from the tower as shown. Which hits the ground with the greatest speed? Ignore Air Resistance. a. Dropped Ball b. Shot Ball c. Same d. Can not say from given information. 5. The magnitude of a vector cannot be smaller than the magnitude of any of its components. TRUE FALSE Short Problems. 10 points each. Show work for any credit. Box final answers. Circle Best Answer. 1. If C = [10 m, 30 ] and D = [25 m, 130 ], what is the magnitude of the sum of these two vectors? a. 20 m b. 35 m c. 15 m d. 25 m e. 50 m 2. and the direction? a. 17 b. 73 c. 107 d. 163 e. 100

2 2. A 0.20-km wide river has a uniform flow speed of 4.00 m/s toward the east. It takes 20.0 s for a boat to cross the river to a point directly north of its departure point on the south bank. In what direction must the boat be pointed in order to accomplish this? Sketch and label the vectors and write the vector equation representing the relative motions. a. 23 west of north b. 22 west of north c. 24 west of north d. 20 west of north e. 17 west of north 4. An airplane flies horizontally with a speed of 300 m/s at an altitude of 400 m. Assume that the ground is level. At what horizontal distance from a target must the pilot release a care package so as to hit the target? Sketch situation. a. 3.0 km b. 2.4 km c. 3.3 km d. 2.7 km e. 1.7 km

3 Long Problems. (25 pts each) Show all your work for full credit. Box final answers. Make it neat and easy to grade. Assume 3 significant figures. Ignore air resistance. 1. A water balloon gun is held 1.40 m above the ground and pointed 25 degrees above the horizontal. It shoots a water balloon that lands on the ground 4.4 m away in the horizontal direction. a) Sketch the event, labeling EVERYTHING, including the initial and final states. State ALL the givens. b) Find the total time the balloon travels in the air. c) Calculate the speed that the water balloon leaves the hose. d) Find the velocity that the balloon hits the ground with, both magnitude and direction.

4 2. Cindy is located at r (2.50 km,30.0 ) and is looking for her dog Benji who is tied to a tree at CO rbo (1.50 km,135 ). Find the Benjii s position relative to Cindy, r BC, in two ways: 1. The Graphical Method: Draw the three vectors in a reference frame, carefully labeling everything and measure the magnitude and direction of Benjii s displacement vector relative to Cindy. Use graph paper if you like. Be sure to state conversion factors and convert your answer back!!! 2. Component Method: Express the vectors in terms of components. What is the equation for the relative position? Write it and then solve for r BC and express your answer in polar coordinates. 3. How close are your results from the two methods? Calculate the percent difference between the polar coordinates of each method. Your results should agree within a percent or tow of each other. Be neat! Put your final answers in the box. Component Method Results: Graphical Method Results: Percent Difference: Graphical Method Results:

5 EXTRA CREDIT! (10 points) A quarterback throws a football straight toward a receiver with an initial speed of 20.0m/s, at an angle of 35.0 above the horizontal. At that instant, the receiver is 20.0 m in front (down field) of the quarterback. With what constant speed should the receiver run in order to catch the football at the level at which it was thrown? Show all your work. Box your answers. Sketch and label.