Force Vectors and 2D Motion
1) Consider the following four force vectors:
Ḟ1 = 10.0 Newtons, due East
Ḟ2 = 40.0 Newtons, due East
Ḟ3 = 30.0 Newtons, due West
Ḟ4 = 50.0 Newtons, due West
(a) Which two vectors add together to give a resultant with the largest magnitude? What is that magnitude?
(b) Which two vectors add together to give a resultant with the smallest magnitude? What is that magnitude?
2) A jetliner is moving at a speed of 170 m/s. The vertical component of the plane's velocity is 97 m/s.
Determine the magnitude of the horizontal component of the plane's velocity.
3) A volley ball is spiked so that it has an initial velocity of 58 ft/s directed downward at an angle of 48° below the horizontal. What is the horizontal component of the ball's velocity when the opposing player fields the ball?
4) An ocean liner leaves New York City and travels 33° North of East for 75 mi. How far East and how far North has it gone? In other words, what are the components of the ship's displacement vector in the directions (a) due East and (b) due North?
5) The magnitude of a force vector Ḟ is 85 pounds (lb). The x component of this vector is directed along the +x axis and has a magnitude of 57 lb. The y component points along the +y axis.
(a) Find the angle between Ḟ and the +x axis.
(b) Find the component of Ḟ along the +y axis.
6) Two bicyclists, starting at the same place, are riding toward the same campground by different routes. One cyclist rides 1680 ft due north and then turns due east and travels another 1460 ft before reaching the campground. The second cyclist starts out by heading due north for 1280 ft and then turns and heads directly toward the campground.
(a) At the turning point, how far is the second cyclist from the campground?
(b) What direction, measured as a positive angle relative to due east, must the second cyclist head during the last part of the trip?
7) See Problem7.png
The magnitudes of the four displacement vectors shown in the drawing are:
A = 26 m, B = 18 m, C = 18 m, and D = 43 m.
Determine the (a) magnitude and (b) direction for the resultant that occurs when these vectors are added together. Specify the direction as an angle measured from the +x axis.
8) A major-league pitcher can throw a ball at 148 ft/s. If a ball is thrown horizontally at this speed, how far will it drop by the time it reaches a catcher who is 63.0 ft away from the point of release?
9) A car drives horizontally off the edge of a cliff that is 57 m high. The police at the scene of the accident note that the point of impact is 92 m from the base of the cliff. How fast was the car traveling when it drove off the cliff?
10) A rock is launched at a speed of 81 m/s from ground level, at an angle of 54° above the horizontal. The rock is fired toward a wall which is located 28 m away. The wall is 32 m high. By how much does the rock clear the top of the wall?