Please Note: It may not always be possible to include the necessary special characters, superscripts, subscripts, etc. in e-mail responses to this group of exercises. We suggest that you discuss this matter with your professor/class and decide upon a system for indicating such characters. You may cut/paste some characters and/or Greek letters from Microsoft Word, using the Insert menu. Alternatively, we suggest that you agree upon abbreviations for or spell out symbols, Greek letters, or characters and indicate superscripts and subscripts by using "sup", "sub", or up/down carats.

Consider the displacement vectors: A = 5 m 30° N of E and C_x = 2 m, C_y = - 4 m

1			The x and y components (including sign) of A Need a Hint?
2			The magnitude of the vector C Need a Hint?
3			The direction of the vector C Need a Hint?
4			The angle between the direction of A and C Need a Hint?
5			The x and y components of A - C Need a Hint?
6			The magnitude of A - C Need a Hint?
7			The direction of A - C Need a Hint?

A 500 N crate is pulled up a frictionless ramp inclined at an angle of 30.0° at a constant speed of 1.00 m/s by a 266 N force which acts at an angle of 20.0° with respect to the ramp.

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W = 500 N F = 266 N θ = 30.0° α = 20.0° v = 1.00 m/s

8			Component of the crate's weight W perpendicular to the ramp Need a Hint?
9			Component of the force F perpendicular to the ramp Need a Hint?
10			The net force on the crate perpendicular to the ramp Need a Hint?
11			Normal force the surface of the ramp exerts on the crate Need a Hint?
12			Component of the crate's weight acting down the ramp Need a Hint?
13			Component of the force F parallel to the ramp Need a Hint?
14			The net force on the crate parallel to the ramp Need a Hint?
15			Acceleration of the crate parallel to the ramp Need a Hint?
16			Speed of the crate after it has been pulled 2.00 m up the ramp Need a Hint?
17			Time it takes to pull the crate 2.00 m up the ramp Need a Hint?

A baseball is thrown off a dormitory roof. The building is 50.0 m high and the ball is thrown with a velocity vo = 30.0 m/s at 60.0° above the horizontal.

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18			The x and y components of the initial velocity Need a Hint?
19			The x and y components of the ball's acceleration the instant it is released Need a Hint?
20			The time it takes the ball to reach the top of its trajectory Need a Hint?
21			The maximum height (with respect to the ground) of the ball Need a Hint?
22			The ball's velocity at the top of its trajectory Need a Hint?
23			The x and y components of the ball's acceleration at the top of its trajectory Need a Hint?
24			The time it takes the ball to get back down to its initial height Need a Hint?
25			The x and y components of the ball's velocity when it is back at the initial height Need a Hint?
26			The time of flight Need a Hint?
27			The magnitude of the impact velocity Need a Hint?
28			The direction of the impact velocity Need a Hint?
29			The range Need a Hint?

A girl can row a boat 2.20 m/s in still water. She wishes to cross a 100 m wide river at a point where the flow rate is 1.50 m/s. If she keeps the boat headed straight across, determine the following:

30			The time it takes her to get across the river Need a Hint?
31			The distance down stream where she lands Need a Hint?
32			Her velocity relative to the ground while she is crossing the river Need a Hint?

If she wants to land directly across the river from her starting position, determine the following:

33			Heading of the boat as she crosses the river Need a Hint?
34			Her velocity relative to the ground while she is crossing the river Need a Hint?