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- The velocity vector of a sprinting cheetah has x- and y-components vx = +28.6 m/s and vy = −26.3 m/s. What is the magnitude of the velocity vector?(a) What is the magnitude of the vector (17î − 27) m/s?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 remote-controlled car is moving around in a level (horizontal) parking lot. The velocity of the car as a function of time is given by: 3 = [5.0m/s – (0.018m/s³)t²]î + [2.0m/s + (0.55m/s²)t]j where î and ĵ are unit vectors representing two perpendicular directions on the horizontal ground (think of them as the East and North directions, if that helps you). b). What are the magnitude and direction of the car's velocity at t = 8.0 s? c). What are the magnitude and direction of the car's acceleration at t = 8.0 s? (Don't be intimated by the velocity function! Look at the î and ĵ components, and work each component separately to begin with, before combining components together to get any resultant vectors, if needed.)Problem 8: Consider two vectors A and B, expressed in unit vector notation as A= aji+ azj and B = bji+ bzj. A. Part (a) Enter an expression for the vector sum A + B in terms of quantities shown in the expressions above. A+B = B 7 8 HOME a i j k 4 5 6 a1 a2 bị 1 2 3 b2 d + END - h VO BACKSPACE CLEAR m DEL Submit Hint Feedback I give up! Hints: 0% deduction per hint. Hints remaining: 2 Feedback: 0% deduction per feedback. Part (b) Enter an expression for the difference vector A - B in terms of quantities shown in the expressions above. Part (c) Enter an expression for the square of the magnitude of the sum vector |A + B| in terms of quantities shown in the expressions above.A velocity vector has a magnitude of 1.85 m/s and makes an angle of 155 ̊ with the +x axis.(a) Sketch a diagram of the vector and show the x and y components.(b) Calculate the x and y components of the vector.
- The vector position of a particle varies in time according to the expression F(t)=(1.41 t + 1.72)i +(0.224t2 + 1.11)J where r is in meters and t is in seconds. Find the speed of the particle in m/s at 2.58 s.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 = 17.0t and y = 4.20t − 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 = 3.24 s. = m = m/s = m/s2An object has an initial velocity of 29.0 m/s at 95.0° and an acceleration of 1.90 m/s2 at 200.0°. Assume that all angles are measured with respect to the positive x-axis. (a) Write the initial velocity vector and the acceleration vector in unit vector notation. (b) If the object maintains this acceleration for 12.0 seconds, determine the average velocity vector over the time interval. Express your answer in your unit vector notation.
- 1At a football game, imagine the line of scrimmage is the y-axis. A player, starting at the y-axis, runs 8.50 yards, back (in the −x-direction), then 15.0 yards parallel to the y-axis (in the −y-direction). He then throws the football straight downfield 55.0 yards in a direction perpendicular to the y-axis (in the +x-direction). What is the magnitude of the displacement (in yards) of the ball? yards (b) What if? The receiver that catches the football travels 64.0 additional yards at an angle of 45.0° counterclockwise from the +x-axis away from the quarterback's position and scores a touchdown. What is the magnitude of the football's total displacement (in yards) from where the quarterback took the ball to the end of the receiver's run?3.1