The position of a particle is given by r(f) = Acos(wt)i + Asin(wt)j + ctk, where A is a constant with units of meters. w is a constant with units of rad/s, and c is a constant with units of m/s. What is the velocity vector? | What is the acceleration vector?
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- Check Your Understanding For vector in a rectangular coordinate system, use Equation 2.29 through Equation 2.32 to show that and .Given: x - coordinate: x = -5.00sinwt, where w is constant, x is meters, andt is seconds y - coordinate: y = 4.00 - 5.00coswt, where w is constant, y in meters, andt seconds What is the expression for position vector? O A. [(-5.00sinwt)î + (4.00 - 5.00coswt)j]m O B. [(5.00sinwt)î + (4.00 - 5.00coswt)j]m ° c. [(5.00sinwt)i + (4.00 + 5.00coswt)j]m O D. [(-5.00sinwt)î + (4.00 + 5.00coswt)j]m22. Three displacement vectors of a cro- quet ball are shown in Figure P3.22, where A 40.0 units, and |C (a) the resultant in unit-vector nota- 20.0 units, B 30.0 units. Find A. 45.0° tion and (b) the magnitude and direc- tion of the resultant displacement. 45.0 23. (a) Taking A = (6.00 i - 8.00 j) units, QIC B (-8.00 i + 3.00 j) units, and C = (26.0 i + 19.0 j) units, determine a Figure P3.2 and b such that a A + bB + C = 0. (b) A student has learned that a single equation cannot be solved to determine values for more than one unknown in it. How would you explain to him that both a and b can be determined from the single equation used in part (a):
- IT.0.0a Given an acceleration vector, initial velocity (uo.Vo), and initial position {xo.yo}, find the velocity and position vectors for t2 0. a(t) = (cos t,5 sin t. (Uo Vo) = (0,5) , (Xo.Yo) = (2.0) What is the velc | vector? v(t) =| Suppose D =Á – B where vector Á has components A, = 5, A, = 2 and vector B has components Bz= -3, B,=-5. a. What are the x- and y-components of vector D? b. Draw a coordinate system and on it show vectors Á, B, and Ď. c. What are the magnitude and direction of vector Ď?sin(20) where vo is the initial velocity in feet per second and is the angle of elevation. If yo 2300 feet per second and is changed from 13° to 14° use differentials to approximate the change in the range. Round your answer to the nearest integer. The range R of a projectile is R = Select one: Ⓒa. 2811 ft X b. 2593 ft C. 5623 ft d. 4568 ft 5186 ft e. = Incorrect 32
- Given: X - coordinate: x = -5.00sinwt, where w is constant, xis meters, andt is seconds y - coordinate: y = 4.00 - 5.00coswt, where w is constant, y in meters, andt seconds What is the expression for velocity vector? O A. 5w(coswti+sinwi) O B. 5w(-coswtî+sinwî) O C. 5w(coswti-sinwj) O D. 5w(-coswti-sinwî)Given: X- coordinate: x= -5.00sinwt, where w is constant, x is meters, and t is seconds y - coordinate: y = 4.00 - 5.00coswt, where w is constant, y in meters, and t seconds What is the expression for position vector? O A. [(5.00sinwt)î + (4.00 - 5.00coswt)j]m O B. [(-5.00sinwt)i + (4.00 - 5.00coswt)j]m O C. [(-5.00sinwt)i + (4.00 + 5.00coswt)j]m O D. [(5.00sinwt)î + (4.00 + 5.00coswt)j]mGiven vector U=2ï+3j°and vector W=5j, , what is 3U+W? O 6i+14j O lli-9j O 6i-14j O lli+9j Next PREDE
- Neglecting frictional forces, the range of a projectile fired at an angle (degrees) above the horizontal with initial velocity Vo (feet per second) is given by R = v sin 20 32 Find and evaluate each of the π following (to 2 significant digits) when = radians and V₁ = 2000 feet per second, then interpret 36 its meaning: OR a. dvo b. ƏR 20VectorA⃗points in the negativeydirection and has a magnitude of 6 units. VectorB⃗has twice the magnitude and points in the positivexdirectionFind the direction and magnitude ofB⃗−A⃗.Express your answer as a whole number. and Express your answer using two significant figures.13. | Let A = 2î + 3j, B = 2î - 4j, and C = A + B. a. Write vector C in component form. b. Draw a coordinate system and on it show vectors A, B, and C. c. What are the magnitude and direction of vector C?