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1 Review for Exam 1 Review for Exam 1 Example Example What tank level would indicate an average speed of 90 mph? a. 3/4 full b. 1/2 full c. 1/4 full d. 1/8 full e. empty MOM, YOUR CAR HOLDS HOW MANY HOLDS HOW MANY GALLONS OF GAS? AND IT GETS HOW MANY MILES PER GALLON? ABOUT 15. ABOUT 25. AND WAS YOUR GAS AND WAS YOUR GAS TANK FULL WHEN TANK FULL WHEN PETER TOOK IT TO PETER TOOK IT TO RUN ERRANDS? RUN ERRANDS? AND PETER HAD IT OUT FOR HOW LONG? YES. MAYBE MAYBE TWO TWO HOURS AND THE TANK IS TANK IS HALF FULL NOW? NOW? LET ME GO CHECK. WELL, SOMEBODY TOLD HER HOW FAST I WAS FAST I WAS DRIVING! DON ’T LOOK T LOOK AT ME. AT ME. SO YOU ’RE RE GROUNDED FOR HOW HOW MANY CENTURIES? CENTURIES? = =− = 1 gallon 90 miles 2 hours 7.2 gallons (used) 1 h 25 miles gas left 15 7.2 7.8 gallons (left) Example: Dot product Which pair of vectors will have the largest value for A · B ? a A B c A B | A |=| B |=5 | A |=| B |=5 b A B | A |=| B |=5 60° d A B | A |=| B |=3 30° e A B | A |=| B |=3 10° A · B = 0 A · B = 25 cos60 = 12.5 A · B = 0 A · B = 9cos30 (< 9 < 12.5) A · B = 9cos10 (< 9 < 12.5) Example: 1D motion An object moves along the x -axis as follows: ( t ) = 25 + (10 m/s) – (30m/s 3 ) t 3 a) At what time ( > 0) does the object stop? Velocity = 0 =⇒ = == 2 0 10 90 0 10 0.33 s 90 vt () 32 ( ) 10 m/s 90 m/s dx t dt a. 0 s b. 0.33 s c. 3.3 s d. 10 s e. 33 s

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2 Example: Free fall A. 3.3 m B. 9.8 m C. 120 m D. 240 m E. 480 m A ball is thrown vertically up into the air (hard!) and comes back down to its starting position 14 s later. At the highest point of its trajectory, how high was the ball? t 0 = 0 v 0 ? y 0 = 0 top = 0 top ? f = 14 s f ? f = 0 A ball is thrown vertically up into the air (hard!) and comes back down to its starting position 14 s later. At the highest point of its trajectory, how high above the starting position was the ball? 0 = 0 0 ? 0 = 0 top = 0 top ? f = 14 s f ? f = 0 target 22 0 2 vv gy −= −∆ To find top , I can use: ? 2 00 1 2 yvt gt =+ − [ Use for the final situation: 2 0 2 0 1 2 (9.8 m/s )(14 s) 68.6 m/s ff f vt gt =+ == = ] Then, () top 0 2 2 0 top 2 020 68.6 m/s 240 m ( 9 . 8 m / s ) vg g = (Answer D) a. 2.5 s b. 5.0 s c. 10 s d. 20 s e. 40 s Example: Projectiles A projectile is fired from a cannon at a 30-degree angle with the ground and an initial velocity of 100 m/s. Assuming no air resistance
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