A river is moving east at 5 m/s. A boat starts from the dock heading 40◦ south of east at 8 m/s. If the river is 2000 m wide, (a) what is the velocity of the boat with respect to Earth and (b) how long does it take the boat to cross the river?

An athlete needs to get across a river. he must reach from point A on one side to point B, directly across from point A on the opposite side. If he wishes to minimize the total time T it would take to do so, at what angle upstreams (measured from the line AB) should he swim? His swimming speed relative to the water is 2.0 mi/h, and his running speed along the bank is 5 mi/h. The river flows downstream at 1.5 mi/h. (The athlete must swim first from point A, then run to reach point B.)

An archer aims at a target that is a horizontal distance 55.0 m away and 5.0 m above the ground. The archer launches her arrow from of height of 1.5 m off the ground, and the arrow hits the target. The arrow is completely horizontal after sticking to the target (i.e., the arrow was traveling horizontally just before hitting the target). What was the initial speed of the arrow, in m/s?

Suppose that a particle begins its motion from the origin and meets the velocity (in m / s) given by: vx (t) = 2.50t vy (t) = 3.50√t.    for t> 0 in seconds. Find the speed of the particle at t = 5.00 s  What is the acceleration vector (in rectangular components) at t = 2.00 s ? Find the magnitude of the displacement between t = 0.00 s and t = 6.00 s