1) Jason Statham jumps off of a diving board which is 3.0 mabove the water surface. He lands traveling at 8.90 m/s at an angleof 75° with respect to the horizontal. (a) What was his initialtake-off speed and direction? (b) Use the Order of Magnitudesense-making technique to check the validity of your answer to part(a).
2) An astronaut shipwrecked on a distant planet with unknowncharacteristics is on top of a cliff, which she wishes to descend.She does not know the acceleration due to gravity on the planet,and she has only a good watch with which to make measurements. Shewants to learn the height of the cliff, and to do this she makestwo measurements. First, she lets the rockfall from rest off thecliff edge; she finds that the rock takes 2.54 s to reach thedistant ground below the cliff. Second, she releases the rock fromthe same spot but tosses it upward so that it rises 2 m beforefalling to the distant ground below the cliff; this time the rocktakes 3.77 s to reach the ground. (a) What is the height of thecliff? (b) What planet in our solar system is this? (c) Use theKnown Values sense-making technique to verify your answer to part(b).
3)While bowling, you throw the bowling ball forward down theright side of the lane. The ball has a constant forward velocity of8.9 m/s. A bowling lane is 18.3 meters long and 1.05 meters wide.Since you are a professional bowler, you release the ball with aspin that causes the ball to accelerate to the left at a constantrate, a. To get a strike, you need your bowling ball to hit theheadpin which is sitting at the end of the lane in the center. (a)What acceleration is needed to hit the headpin? (ignore the widthof the pin and ball) (b) What is the final speed of the ball? (c)Use the Order of Magnitude sense-making technique to check thevalidity of your answer to part (b)
4) Gerry the gerbil walks 55 cm in the positive y-direction.After this, he is located 95 cm from the origin at an angle of 50°from the +xaxis towards the +y-axis, as shown in the figure. (a)Complete the figure by including the change in position and theinitial position vectors. (b) Calculate Gerry’s initial position.(c) Use the Related Quantities sense-making technique to check thevalidity of your answer.
5) Deserted on a deserted Island you spot a slightly exposed tincan under a tree. Upon opening it you find it’s instructions to atreasure. It reads: “Ten paces from this very tree in a directiontwenty degrees south of west lies the first location. Ten pacesfrom this very tree in a direction sixty degrees north of east liethe second location. Walk from this tree exactly the distance anddirection you would walk from the first location to the secondlocation and you will find ye treasure. Yar†(a) What are thecoordinates of treasure? (b) Use a physical representation inconjunction with the Related Quantities sense-making technique tocheck the validity of your answer.
