1. A grasshopper leaps into the air from the edge of a vertical cliff, as shown in figure below. Find (a) the initial speed of the grasshopper and (b) the height of the cliff. sin50.0°=0.76, cos50.0°=0.64 6.74 cm 50.0 Not to scale

3. Is it possible for two vectors, A and B, of unequal magnitudes to have a resultant with a magnitude less than the magnitudes of either A or B? Explain your answer. You may use illustrations,

Two velocity vectors are defined as follows: ₁ = 40.0 m/s, 50.0° cw from the +x axis v₂ = 30.0 m/s, 75.0° cw from the -y axis a) b) Sketch the vector ₁ on an x-y grid. Label any relevant angle. Calculate the x- and y-components of ₁. Write the vector in terms of its components using unit vector notation. c) d) e) v₂ – v- Calculate the x- and y-components of the change in velocity defined as A = Write the vector Av in terms of its components using unit vector notation. Sketch the vector A on an x-y grid. Define a relevant angle symbolically whose numerical value you will calculate in the next part. f) g) Calculate the magnitude and direction of the vector Av. h) Finally, write the vector Av in terms of its magnitude and direction. Sketch the vector v₂ on an x-y grid. Label any relevant angle. Calculate the x- and y-components of 7₂. Write the vector ₂ in terms of its components using unit vector notation.

In the sport of billiards, event organizers often remove one of the rails on a pool table to allow players to measure the speed of their break shots (the opening shot of a game in which the player strikes a ball with his pool cue). V. o h d The top of a pool table is a height h = 3.25 ft from the floor. If a player's ball lands a distance d 14.75 ft from the table edge, what is her break shot speed vo? 12.3 Vo = mph Incorrect At what speed v did her pool ball hit the ground? 4.21 mph = Incorrect

Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. If these two vectors are added together, the magnitude of the sum... A) is equal to 2.0 m. B) could be as small as 2.0 m or as large as 12 m. C) is equal to 12 m. D) is equal to 8.6 m

Number 6

4. Swims across Lake Erie are officially sanctioned by the Lake Erie Open Water Swimming Association. Your friend on the swim team wants to swim across the lake. The plan is that your friend will swim to Presque Isle starting at a location at Long Point, Ontario which is 24 miles due north of Presque Isle. You will be navigating a boat with a GPS. Your friend can maintain a speed of 1.80 mph in still water. All during the swim you observe that objects drifting in the water are moving at 0.70 mph to the east due to the current. a. What bearing should you maintain? That is what direction should you point the boat to reach Presque Isle? Give your answer relative to a compass direction (i.e., 30° north of west). Hint, you want your net velocity vector to be straight south. b. How long did it take your friend to swim across Lake Erie? c. What is the addition amount of time that your friend will need to swim compared to if there was no current (assume your friend swims at a constant rate)?

A ball was dropped from a rooftop measuring 4.4 m above the ground. How long will it take for it to hit the ground? Select one: O a. 1.1365 s O b. 0.9471 s O c. 0.7577 s O d. 0.8970 s

Three force vectors are added together.  One has a magnitude of 9 N, the second one a magnitude of 18 N, and the third a magnitude of 15 N.  What can we conclude about the magnitude of the net force vector?  Explain. I.       It must equal 42 N. II.     It cannot be 0 N.      III.    Anything from –42 N to +42 N.  IV.    It can be anything from 0 N to 42 N. V.     None of the above can be concluded.

Given the vectors Ā = (2î – j) N and B = (3î + j)m. Then, 3A B equals O a. -5 N- m O b.15 N m OC. 5N m O d. -15 N· m