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Name Date Pd Particle Models in Two Dimensions Worksheet 3: Projectile Motion Problems FOR ALL PROBLEMS USE SUBSCRIPTS TO DISTINGUISH X & Y DIRECTIONS 1. The movie "The Gods Must Be Crazy" begins with a pilot dropping a bottle out of an airplane. A surprised person below, who thinks it is a message from the gods, recovers it. If the plane from which the bottle was dropped was flying at a height of 500m, and the bottle lands 400m horizontally from the initial dropping point, how fast was the plane flying when the bottle was released? LABELED SKETCH with MOTION DIAGRAM KNOWN QUANTITIES y 500m x 400m a x 0m / s / s a y 10m / s / s UNKNOWNS t vix viy 0m / s POSSIBLE EQUATIONS 1 y a y t 2 viy t 2 1 m m 500m (10 2 )(t 2 ) 0 t 2 s s 2 100 t 10 t x vix t 400m vix (10 s ) 40 m vix s 2. Suppose that an airplane flying 60 m/s, at a height of 300m, dropped a sack of flour. How far from the point of release would the sack have traveled when it struck the ground? Where will the plane be in relation to the sack when the sack hits the ground? Illustrate your answer carefully using the grid provided. ©Modeling Instruction 2013 1 U6 2D Motion - ws 3 v3.1 KNOWN QUANTITIES m vix 60 s y 300m a x 0m / s / s a y 10m / s / s viy om / s UNKNOWNS t and ∆x POSSIBLE EQUATIONS 1 y a y t 2 viy t 2 1 m m 300m (10 2 )(t 2 ) 0 t 2 s s 2 60 t 7.7 s t x vix t x 60m / s(7.7 s) x 464m 3. Tad drops a cherry pit out the car window 1.0 m above the ground while traveling down the road at 18 m/s. How far, horizontally, from the initial dropping point will the pit hit the ground? If the car continues to travel at the same speed, where will the car be in relation to the pit when it lands? LABELED SKETCH with MOTION DIAGRAM Pit should land right below his hand because the pit has the same constant velocity in the x-dir as the car. ©Modeling Instruction 2013 2 U6 2D Motion - ws 3 v3.1 KNOWN QUANTITIES UNKNOWNS m s y 1m a x 0m / s / s t and ∆x vix 18 a y 10m / s / s viy om / s POSSIBLE EQUATIONS 1 y a y t 2 viy t 2 1 m m 1m (10 2 )(t 2 ) 0 t 2 s s 2 0.2 t x vix t x 18m / s (0.45s ) x 8.1m 0.45s t 4. A student finds that it takes 0.20s for a ball to pass through a set of timers a distance of 0.3 m apart on a level ramp. The end of the ramp is 0.92 m above the floor. a. What is the speed of the ball when it is passing through the timers? KNOWN QUANTITIES UNKNOWNS POSSIBLE EQUATIONS b. Where should a coin be placed so that the ball strikes it directly on impact with the ground? KNOWN QUANTITIES UNKNOWNS POSSIBLE EQUATIONS 5. Suppose now that the same ball, released from the same ramp (0.92 m high) struck a coin placed 0.25 m from the end of the ramp. a) What was the ball's horizontal velocity? KNOWN QUANTITIES UNKNOWNS POSSIBLE EQUATIONS b) How long did it take for the ball to pass through the same set distance of 0.3 m? ©Modeling Instruction 2013 3 U6 2D Motion - ws 3 v3.1 KNOWN QUANTITIES ©Modeling Instruction 2013 UNKNOWNS 4 POSSIBLE EQUATIONS U6 2D Motion - ws 3 v3.1