A wall clock has a minute hand with a length of 0.51 m and an hour hand with a length of 0.27 m. Take the center of the clock as the origin, and use a Cartesian coordinate system with the positive x axis pointing to 3 o'clock and the positive y axis pointing to 12 o'clock. Express the position vectors of the tip of the hour hand (A) and the tip of the minute hand (B) at the following times. (a) 12:00 A = ( 0.51 |× m) positive y B = (0.21 x m) positive y (b) 3:00 A = ( 0.51 |× m) positive x v B = (0.27 x m) positive y (c) 6:00 A = (0.51 |× m) negative y %3! B = (-0.27 x m) positive y (d) 9:00 A = (0.51 |× m) negative x v B = (-0.27 |× m) negative y %3! Let the +y direction be straight up and the +x direction be to the right.

A wall clock has a minute hand with a length of 0.51 m and an hour hand with a length of 0.27 m. Take the center of the clock as the origin, and use a Cartesian coordinate system with the positive x axis pointing to 3 o'clock and the positive y axis pointing to 12 o'clock. Express the position vectors of the tip of the hour hand (A) and the tip of the minute hand (B) at the following times. (a) 12:00 A = ( 0.51 |× m) positive y B = (0.21 x m) positive y (b) 3:00 A = ( 0.51 |× m) positive x v B = (0.27 x m) positive y (c) 6:00 A = (0.51 |× m) negative y %3! B = (-0.27 x m) positive y (d) 9:00 A = (0.51 |× m) negative x v B = (-0.27 |× m) negative y %3! Let the +y direction be straight up and the +x direction be to the right.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter1: Introduction And Vectors

Section: Chapter Questions

Problem 35P

See similar textbooks

Similar questions

Consider the three displacement vectors A=(3i3j)m, B=(i4j)m, and C=(2i+5j)m. Use the component method to determine (a) the magnitude and direction of the vector D=A+B+C and (b) the magnitude and direction of E=AB+C.
Find the components of the acceleration vector a in spherical coordinates.
The minute hand of a wall clock measures 10 cm from its tip to the axis about which it rotates. The magnitude and angle of the displacement vector of the tip are to be determined for three time intervals. What are the (a) magnitude and (b) angle from a quarter after the hour to half past, the (c) magnitude and (d) angle for the next half hour, and the (e) magnitude and (f) angle for the hour after that?
A velocity vector, with magnitude v= 50.8m/s , is directed vertically upwards. The coordinate axes are chosen such that the x axis is rotated clockwise by an angle θ= 45.6∘ below the horizontal, as shown. What is the x component, in meters per second, of the velocity vector, v→? What is the y component, in meters per second, of the velocity vector, v→?
Calculate the magnitude and direction of the resultant of the two vectors a) 50 km E and b) 70 km 60* NE.2) An airplane travels at 4.5 x 10^2 km due east and then travels an unknown distance due north. Finally, it returns to its starting point by travelling a distance of 525 km. How far did the airplane travelled due north?
From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 7.50 m/s and angle of 18.0° below the horizontal. It strikes the ground 5.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: y0. Assume SI units. Do not substitute numerical values; use variables only.) xi = − yi = (c) Find the equations for the x- and y-components of the position as functions of time. (Use the following as necessary: y0 and t. Assume SI units.) x = y = (f) How long does it take the ball to reach a point 10.0 m below the level of launching?
A watermelon seed has the following coordinates: x = -3.3 m, y = 8.9 m, and z = 0 m. Find its position vector as (a) a magnitude and (b) an angle relative to the positive direction of the x axis. If the seed is moved to the xyz coordinates (1.8 m, 0 m, 0 m), what is its displacement as (c) a magnitude and (d) an angle relative to the positive direction of the x axis? Put the angles in the range (-180°, 180°].
From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 9.50 m/s and angle of 15.0° below the horizontal. It strikes the ground 6.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: y0. Assume SI units. Do not substitute numerical values; use variables only.) xi =____ yi =_____ (b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity. vi, x =____ m/s vi, y =____ m/s c) Find the equations for the x- and y-components of the position as functions of time. (Use the following as necessary: y0 and t. Assume SI units.) x =______ m y =_______ m (d) How far horizontally from the base of the building does the ball strike the ground? ___m (e) Find the height from which the…
Suppose you walk 18.0 m straight west and then 25.0 mstraight north. How far are you from your starting point, andwhat is the compass direction of a line connecting yourstarting point to your final position? (If you represent the twolegs of the walk as vector displacements A and B , then this problem asks you to find their sumR = A + B .)
A hiker begins a trip by walking 25 km southwest from the base camp. On the next day she walks 40km in a direction 60 degrees north of east, at which point she discovers a forest rangers' tower. Determine the magnitude and direction of the hiker's resultant displacement using the cosine and sine law.
From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 8.80 m/s and angle of 16.0° below the horizontal. It strikes the ground 4.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: y0. Assume SI units. Do not substitute numerical values; use variables only.) xi = yi =
Using the Pythagorean theorem and the graphical method, calculate the resultant vector of the following (b) 20N to the east, 20N to the west and 10N to the north