Question

1) Jason Statham jumps off of a diving board which is 3.0 m above the water surface. He lands traveling at 8.90 m/s at an angle of 75° with respect to the horizontal. (a) What was his initial take-off speed and direction? (b) Use the Order of Magnitude sense-making technique to check the validity of your answer to part (a).

2) An astronaut shipwrecked on a distant planet with unknown characteristics 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. She wants to learn the height of the cliff, and to do this she makes two measurements. First, she lets the rockfall from rest off the cliff edge; she finds that the rock takes 2.54 s to reach the distant ground below the cliff. Second, she releases the rock from the same spot but tosses it upward so that it rises 2 m before falling to the distant ground below the cliff; this time the rock takes 3.77 s to reach the ground. (a) What is the height of the cliff? (b) What planet in our solar system is this? (c) Use the Known Values sense-making technique to verify your answer to part (b).

3)While bowling, you throw the bowling ball forward down the right side of the lane. The ball has a constant forward velocity of 8.9 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 a spin that causes the ball to accelerate to the left at a constant rate, a. To get a strike, you need your bowling ball to hit the headpin which is sitting at the end of the lane in the center. (a) What acceleration is needed to hit the headpin? (ignore the width of the pin and ball) (b) What is the final speed of the ball? (c) Use the Order of Magnitude sense-making technique to check the validity 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 the initial position vectors. (b) Calculate Gerry’s initial position. (c) Use the Related Quantities sense-making technique to check the validity of your answer.

5) Deserted on a deserted Island you spot a slightly exposed tin can under a tree. Upon opening it you find it’s instructions to a treasure. It reads: “Ten paces from this very tree in a direction twenty degrees south of west lies the first location. Ten paces from this very tree in a direction sixty degrees north of east lie the second location. Walk from this tree exactly the distance and direction you would walk from the first location to the second location and you will find ye treasure. Yar” (a) What are the coordinates of treasure? (b) Use a physical representation in conjunction with the Related Quantities sense-making technique to check the validity of your answer.

Answer 1

1. Let Jason Statham's initial take of speed is V  at an angle with the horizontal. He lands traveling at v=8.90 m/s at an angle of with respect to the horizontal direction.

Now initial take of speed (V) has two components . Horizontal component and vertical component .

When he lands , his landing velocity also have two components. Horizontal component and vertical component ..

# Analysis of speed along horizontal direction

Since horizontal component of the initial take off speed and landing speed is unaffected by the gravitational acceleration [ as gravitational force is perpendicular to the velocity and hence no work will be done ] , hence horizontal component of the initial take off speed and landing speed are equal. So we get

Or

............(i)

# Analysis of speed along vertical direction

We find that the Jason initial speed along vertical direction was and after travelling a distance 'h' its speed becomes  . Using Newton's law of motion , we find

Or

Or

Or

Or

.........(ii)

From (i) and (ii)m we get

And

(b)

.since i.e final speed is greater than the initial speed when it is under the gravitational acceleration, the final result seems to be correct answer.