Please write solutions for each question.

1. Two vectors are given bya=3.0i^+5.0j^ and b = 2.0i + 4.0j. b=2.0i^+4.0j^Find (a)ab , (b) ab, (c)(a+b)b, and (d) the component ofa along the direction ofb

2. A baseball is hit at ground level. The ball reaches its maximum height above ground level 3.0 s after being hit. Then 2.5 s after reaching its maximum height, the ball barely clears a fence that is 97.5 m from where it was hit. Assume the ground is level. (a) What maximum height above ground level is reached by the ball? (b) How high is the fence? (c) How far beyond the fence does the ball strike the ground?

3) A cat rides a merry-go-round turning with uniform circular motion. At time t1 = 2.00 s, the cat's velocity is V1 = (3.00 m/s) i+ (4.00 m/s) j, measured on a horizontal ty coordinate system. At t2= 5.00 s, the cat's velocity is V2 = (-3.00 m/s) i + (-4.00 m/s) j. What are (a) the magnitude of the cat's centripetal acceleration and (b) the magnitude of the cat's average acceleration during the time interval t2 - t1, which is less than one period?

Answers:

1. a) 2.0k b)26 c)46 d)5.81

2. a) 44.1m b)13.48m c)8.86m

3. 5.24m/s^2 b)3.33m/s^2