SPH4U Grade 12 University Preparation Physics

Kinematics in Two Dimentions Test 3 Knowledge Inquiry Application Communication /20 /16 /10 /5

Section 1: Knowledge & Comprehension (20 marks) 1. Two vectors are shown to the right and defined as and. Which vector below shows the quantity ( –)?

2. Two children are in a race. Janine gives Billy a head start of 3.0 s. Which statement best describes the relationship between the times that each child runs? a. tJ = tB + 3.0 s b. tB = tJ + 3.0 s c. tB = tJ + 3.0 s d. tB = tJ 3. A soccer player successfully kicks a goal through the goalposts located at the east end of the stadium. What are the directions of the instantaneous velocity and acceleration, respectively, of the soccer ball at the peak of its trajectory? a. east, east b. zero (no direction), down c. east, down d. east, up e. down, down

4. Consider the vector diagram shown to the right. Which statement below is correct? a. + = b. + = c. + = d. – = –

5. An object is travelling due south when it experience a uniform acceleration directed east. Its velocity some time later a. must be directed east b. could be directed east c. must be directed south and east d. could be directed south when the acceleration stops e. must be directed east when the acceleration stops

6. In the diagram below, the magnitude of the vertical component of the resultant displacement is

a. 6.1 m b. 9.3 m c. 0.70 m d. 11.1 m e. 1.1 m

7. A student starts 300 m north of the school and ends up 200 m east of the school. Which vector diagram best shows the displacement as calculated by = f – t. Problem Solving 1. Jose Bautista hits the baseball when it is 1.10 m off the ground, giving it an initial velocity of 40.0 m/s at 37.3 above the horizontal. To score a homerun, the ball must cross a 3.00 m high fence which is 104 m away from the batter. Did Bautista score a homer? Prove your result. (2 marks diagram, 4 marks solution).

2. A police officer at the side of the highway sees a bank robber in the get-away vehicle speeding down the road at 35.0 m/s. The officer calls quickly for backup and then starts to follow the robber when the robber is 100 m away from him. If the officer starts from rest and accelerates at 1.40 m/s2, how far will she drive before she catches the robber? Include a diagram (diagram 1 mark, solution 6 marks). Section 2: Application (10 marks) 1. A plane with an airspeed of 100 m/s flies directly north-east. There is a wind blowing at 20 m/s. Consider the possible wind directions below. i. North ii South iii. East iv. West In which of these directions would the wind actually increase the magnitude of the plane’s velocity? a. i b. ii and iv c. none of these d. i and ii e. all of these

2. A person sitting on the back of a pickuo truck has a pitching machine that fires ball backwards out of the truck. The truck is driving 100 km/h forward and the pitching machine is set for 100 km/h. An observer at the side of the road sees the ball a. move forward at 100 km/h b. move forward at 200 km/h c. move backward at 100 km/h d. move backward at 100 km/h e. fall straight down with zero horizontal velocity 3. A plane flying with constant velocity over a remote arctic research station drops a bundle of supplies. Describe and explain the motion of the bundle as it falls in the frame of reference of the pilot AND in the frame of reference of the ground. (3 marks)

4. You are on the desert island shown below, on Skull Mountain. The breeze starts to pick up until hurricane-force winds are blowing south west. Knowing that the winds travel in a counter-clockwise circle around the center of a hurricane, you are able to deduce the location of the storm center and take cover accordingly. Where is the center of the storm? Choose from the points marked W, X, Y and Z below. Explain with reference to vectors. (2 marks) 5. In underwater research vehicle is operating remotely from the shore. The vehicle is heading due south, but the cameras are showing a large wall of rock just ahead so it will need to turn to the west. In what direction must the vehicle operator direct the acceleration of the motor? Explain fully. (2 marks)

Section 3: Thinking & Inquiry (16 marks) 1. A bus is travelling south on Dufferin at 50 km/h. You walk towards the back of the bus at 4.0 km/h relative to the bus. Northbound traffic is approaching the bus at 80 km/h relative to the bus. The relative speed of the traffic approaching you is a. 84 km/h b. 76 km/h c. 34 km/h d. 134 km/h e. 126 km/h 2. A police officer is chasing a bad guy down the street. The bad guy is moving at 6 m/s [E] relative to the ground, but the police officer sees them moving at 2 m/s [W]. What is the velocity of the police officer relative to the ground? a. 3 m/s [E] b. 4 m/s [E] c. 4 m/s [W] d. 8 m/s [W] e. 8 m/s [E]

3. A jet experiences an acceleration of 5g’s (4.50 times the force of gravity) [S 25E] for 2.5 s, after which it is travelling 200 m/s [E]. a) Determine the change in velocity of the jet. (1 mark)

b) Draw a vector diagram that would allow you to find the initial velocity of the jet. Label all vectors clearly and include an equation that corresponds to the diagram. Then determine the initial velocity of the plane. (3 marks, 3 marks) 4. A pilot is flying from Vancouver to Los Angeles, as shown in the diagram below. They leave Vancouver at 6:00 a.m. with an airspeed of 950 km/h and arrive in LA at 8:35 a.m. The speed of the wind is 300 km/h east and the pilot sets a heading of [S30.0W] for the flight. How far from Vancouver is Los Angeles? Include a fully labeled vector diagram and vector addition statement. (7 marks)