Classical Mechanics Answers

Vector A with arrow has a negative x component 2.70 units in length and a positive y component 1.82 units in length.
(a) Determine an expression for A with arrow in unit-vector notation.
( î + ĵ) units

(b) Determine the magnitude and direction of A with arrow.
magnitude unit(s)
direction ° counterclockwise from the positive x axis

(c) What vector B with arrow when added to vector A with arrow, gives a resultant vector with no x component and a negative y component 3.88 units in length?
( î + ĵ) units

The vector A with arrow has x, y, and z components of -11.00, 4.00, and -0.10 units, respectively.
(a) Write a vector expression for A with arrow in unit-vector notation.
(b) Obtain a unit-vector expression for a vector B with arrow one-fourth the length of A with arrow pointing in the same direction as A with arrow.
(c) Obtain a unit-vector expression for a vector C with arrow three times the length of A with arrow pointing in the direction opposite the direction of A with arrow.

Consider the three displacement vectors A with arrow = (2î − 3ĵ) m, B with arrow = (7î − 2ĵ) m, and C with arrow = (-3î + 1ĵ) m. Use the component method to determine the following.
(a) The magnitude and direction of the vector Darrowbold = A with arrow + B with arrow + C with arrow.
magnitude m
direction ° counterclockwise from the +x axis
(b) The magnitude and direction of E with arrow = −A with arrow − B with arrow + C with arrow.
magnitude m
direction ° counterclockwise from the +x axis

A novice golfer on the green takes three strokes to sink the ball. The successive displacements of the ball are d1 = 4.10 m to the north, d2 = 2.10 m northeast, and d3 = 0.90 m at θ = 30.0° west of south (figure below). Starting at the same initial point, an expert golfer could make the hole in what single displacement?
m
° (north of east)

A force of 50.7 Newtons pulls due west on a structure, and a second force of 81.3 Newtons pulls S 21o W. Find the principle angle of the resultant.

Round the answer to 2 decimal places.

A pilot flies with a heading of N 53o E, and its air speed is 154.8 miles/h. It is driven from its course by a wind of 396.4 miles/h and travelling S 14o E. Find the principle angle of the resultant.

Round the answer to 2 decimal places.

The shells fired from an artillery piece have a muzzle speed of 215 m/s, and the target is at a horizontal distance of 1.70 km. Two possible angles can be used to hit the target. Find the smallest angle relative to the horizontal at which the gun should be aimed?(Hint: sin2θ = 2sinθcosθ)

a particle is constraint to move 2d on a smooth inclined plane making an angle 90 degree to the horizontal assume that a line of intersection of inclined plane with horizontal plane is the x axis and aline on the inclined plane perpendicular is y axis. obtain lagrangain of the particle in term of coordinate x and y axis?

What is the shape of the graph of acceleration vs. sin theta? What does it imply in the relationship between acceleration and sin theta? What is the slope of the graph related to acceleration due to gravity?

A car travels 1/4 of a circle of radius r .Ratio between distance to its displacement is