A robotic vehicle, or rover, is exploring the surface of Mars. The stationary Mars lander is the origin of coordinates, and the sur- rounding Martian surface lies in the xy-plane. The rover, which we x = 2.0 m - 10.25 m > s22t2 represent as a point, has x- and y-coordinates that vary with time: y = 11.0 m > s2t + 10.025 m > s32t3 (a) Find the rover’s coordinates and distance from the lander at t = 2.0 s. (b) Find the rover’s displacement and average velocity vectors for the interval t = 0.0 s to t = 2.0 s. (c) Find a general S. Express expression for the rover’s instantaneous velocity vector v S at t = 2.0 s in component form and in terms of magnitude and v

Why is (j + k) = i?I see that i x i = 0, that makes sense. But I thought that j x k = i? not j + k.

Y-COMPONENT MAGNITUDE DIRECT1ON -COM PONENT 3341 VECTOR 7.9 7.10 -3 40 16.00 1.10 6.40 -3.40 9.20 18.5 2.1 8.4 3014 319.3 -5:50 7.20 Ry: 8.0 115.3 4 SULTANT R

I want to know if I am on track for problem 1 i)

A golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by  x = 17.2t  and  y = 4.16t − 4.90t2,  where x and y are in meters and t is in seconds. (a) Write a vector expression for the ball's position as a function of time, using the unit vectors î and ĵ. (Give the answer in terms of t.) =         m By taking derivatives, do the following. (Give the answers in terms of t.) (b) obtain the expression for the velocity vector  as a function of time =          m/s(c) obtain the expression for the acceleration vector  as a function of time =          m/s2(d) Next use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the golf ball at t = 3.18 s.   =         m   =         m/s   =         m/s2

A quarterback throws a football while standing at the very center of the field on the 50 yard line. The ball leaves his hand at a height of 5 ft and has initial velocity vo = 51i +37j + 27k ft/s. Assume an acceleration of 32 ft/s² due to gravity and that the i vector points down the field toward the endzone and the j vector points to the sideline. The field is 150 ft in width and 300 ft in length. Determine the position function that gives the position of the ball t seconds after it is thrown. The ball is caught by a player 5 ft above the ground. Assume the player is standing vertically with both toes on the ground at the time of reception. (Use symbolic notation and fractions where needed.) r(t): =

Given vector A = xz ax -xy ay +yz az    Transform A into cylindrical coordinate and it's magnitude at point (1,30o,2) is equal to:

A wall clock has a minute hand with a length of 0.46 m and an hour hand with a length of 0.26 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. Write the vector that describes the displacement of a fly if it quickly goes from the tip of the minute hand to the tip of the hour hand at 3:00 P.M. (Let D represents the displacement of the fly.) D = 0.46 |× mî+ -0.26 Let the +y direction be straight up and the +x direction be to the right. Recall the definition of displacement, and remember that positions are vector quantities.

1

B U Bx = 12.2 cm. Consider vector B pictured below and the given length for Bx = 12.2cm and 0 = 24.0 What is the length (the hypotenuse) of vector B ? 2 51