1)Chinook salmon can cover more distance in less time by periodically making jumps out of the water. Suppose a salmon swimming in still water jumps out of the water with velocity 5.63 m/s at 41.6° above the horizontal, re-enters the water a distance *L* upstream, and then swims the same distance *L* underwater in a straight, horizontal line with velocity 2.62 m/s before jumping out again.

a)What is the fish’s average horizontal velocity (in m/s) between jumps? (Round your answer to at least 2 decimal places.)

b)Consider the interval of time necessary to travel 2*L*. How is this reduced by the combination of jumping and swimming compared with just swimming at the constant speed of 2.62 m/s? Express the reduction as a percentage.

**c)What If?** Some salmon are able to jump a distance *L* out of the water while only swimming a distance L/4 between jumps. By what percentage are these salmon faster than those requiring an underwater swim of distance *L*? (Assume the salmon jumps out of the water with velocity 5.63 m/s at 41.6° above the horizontal, re-enters the water a distance *L* upstream, and then swims a distance L/4 underwater in a straight, horizontal line with velocity 2.62 m/s before jumping out again.)

2)Children playing in a playground on the flat roof of a city school lose their ball to the parking lot below. One of the teachers kicks the ball back up to the children as shown in the figure below. The playground is 4.60 m above the parking lot, and the school building’s vertical wall is h=6.00m high, forming a 1.40 m high railing around the playground. The ball is launched at an angle of theta=53 degree above the horizontal at a point d=24.0m from the base of building wall.The ball takes 2.20 s to reach a point vertically above the wall.

a)Find the speed (in m/s) at which the ball was launched.

b)Find the vertical distance (in m) by which the ball clears the wall.

c)Find the horizontal distance (in m) from the wall to the point on the roof where the ball lands.

**d)What If?** If the teacher always launches the ball with the speed found in part (a), what is the minimum angle (in degrees above the horizontal) at which he can launch the ball and still clear the playground railing? (*Hint*: You may need to use the trigonometric identity sec^{2}( ) = 1 + tan^{2}( ).)(e)

What would be the horizontal distance (in m) from the wall to the point on the roof where the ball lands in this case?

3)Lisa in her Lamborghini accelerates at the rate of (2.80**î** − 4.40**ĵ**) m/s^{2}, while Jill in her Jaguar accelerates at (1.20**î** + 4.00**ĵ**) m/s^{2}. They both start from rest at the origin of an *xy* coordinate system. After 5.00 s, find the following.a) What is Lisa’s speed with respect to Jill?

(b) How far apart are they?

(c) What is Lisa’s acceleration relative to Jill?

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