Express all answers using three significant figures and the appropriate units.

1. A car is driven 240 km west and then 98 km southwest (45).

a) What is the displacement of the car from the point of origin (magnitude)?

b) What is the displacement of the car from the point of origin (direction)?

2. a) If Vx = 9.9 units and Vy = -6.3 units, determine the magnitude of VV.

b) Determine the direction of VV.

4. A tiger leaps horizontally from a 5.6 m -high rock with a speed of 3.9 m/s

a) How far from the base of the rock will she land?

5. A diver running 2.2 m/s dives out horizontally from the edge of a vertical cliff and 2.9 s later reaches the water below.

a) How high was the cliff?

b) How far from its base did the diver hit the water?

6. A ball is thrown horizontally from the roof of a building 7.9 m tall and lands 9.9 m from the base.

a) What was the ball's initial speed?

7. A grasshopper hops along a level road. On each hop, the grasshopper launches itself at angle 0 = 45 and achieves a range R = 0.81 m.

a) What is the average horizontal speed of the grasshopper as it hops along the road? Assume that the time spent on the ground between hops is negligible.

8. A projectile is fired with an initial speed of 36.5 m/s at an angle of 42.2 above the horizontal on a long flat firing range. use three significant number and the right units

a) Determine the maximum height reached by the projectile.

b) Determine the total time in the air.

10. An airplane is heading due south at a speed of 670 km/h

a) If a wind begins blowing from the southwest at a speed of 110 km/h (average), calculate the velocity (magnitude) of the plane relative to the ground. [Hint: First draw a diagram.]

Express your answer to three significant figures and include the appropriate units.

b) Calculate the velocity (direction) of the plane relative to the ground. Express your answer to three significant figures and include the appropriate units.

11. An airplane is heading due south at a speed of 712 km/h. A wind begins blowing from the southwest at a speed of 110 km/h (average)

a) In what direction should the pilot aim the plane so that it will fly due south? Express your answer to three significant figures and include the appropriate units.

12. A swimmer is capable of swimming 0.45 m/s in still water.

a) If she aims her body directly across a 63-mm-wide river whose current is 0.38 m/s, how far downstream (from a point opposite her starting point) will she land? Express your answer to two significant figures and include the appropriate units.

b) How long will it take her to reach the other side? Express your answer to two significant figures and include the appropriate units.

13. A swimmer is capable of swimming 0.72 m/s in still water.

a) At what upstream angle must the swimmer aim, if she is to arrive at a point directly across the stream of a 55-m-wide river whose current is 0.50 m/s? Express your answer to two significant figures and include the appropriate units

b) How long will it take her? Express your answer to two significant figures and include the appropriate units