A small stone is kicked from the edge of a cliff. Its x- and y-coordinates as functions of time are given by x - 19.6t and y = 4.04t – 4.90t?, where x and y are in meters and t is in seconds. (Do not include units in your answer.) (a) Write a vector expression for the stone's position as a function of time (in m), using the unit vectors î and ĵ. (Give the answer in terms of t.) m By taking derivatives, do the following. (b) Obtain the expression for the velocity vector v as a function of time (in m/s). (Give the answers in terms of t.) m/s (c) Obtain the expression for the acceleration vector å as a function of time (in m/s²). m/s?

A small stone is kicked from the edge of a cliff. Its x- and y-coordinates as functions of time are given by x - 19.6t and y = 4.04t – 4.90t?, where x and y are in meters and t is in seconds. (Do not include units in your answer.) (a) Write a vector expression for the stone's position as a function of time (in m), using the unit vectors î and ĵ. (Give the answer in terms of t.) m By taking derivatives, do the following. (b) Obtain the expression for the velocity vector v as a function of time (in m/s). (Give the answers in terms of t.) m/s (c) Obtain the expression for the acceleration vector å as a function of time (in m/s²). m/s?

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 46P: Vector A has x and y components of 8.70 cm and 15.0 cm, respectively; vector B has x and y...

See similar textbooks

Similar questions

Figure OQ1.13 shows two vectors D1 and D2. Which of the possibilities (a) through (d) is the vector D22D1, or (e) is it none of them? Figure OQ1.13
An object is dropped from rest and takes 2.83 seconds to reach the ground below. From what distance above the ground was it dropped? (State this as a positive number and assume it has proper SI Units)
A space shuttle’s coordinates as functions of time are given by x(t) = 7.0 t^3 and y(t) = 4.0t^2 - 2.1t , where x and y are in meters and t is in seconds. Write a vector expression for the ball’s velocity as a function of time.
A space shuttle’s coordinates as functions of time are given by x(t) = 7.0 t^3 and y(t) = 4.0t^2 - 2.1t , where x and y are in meters and t is in seconds. write a vector expression for the ball's position as a function of time.
A space shuttle’s coordinates as functions of time are given by x(t) = 7.0 t^3 and y(t) = 4.0t^2 - 2.1t , where x and y are in meters and t is in seconds. write a vector expression for the ball's acceleration as a function of time.
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 girl delivering newspapers covers her route by traveling 2.75 blocks west, 3.00 blocks north, and then 5.75 blocks east. What is her resultant displacement? What is the total distance she travels?
If Vx = 7.90 units and Vy = -6.20 units, determine (a)the magnitude and (b)direction of V⃗.
The world record for the hundred meter dash is 9.58 s.What is the corresponding average speed in units of m/s,km/h,ft/s,and mi/h? At this speed, how long would it take to run 1.00 x 102 yards?
Harry, an avid TikToker, decided to look at his wristwatch to tell his friend dolphins the current time. However, his dolphins only understand the time if it is stated in terms of the resultant vector when the hour hand and minute hand vectors are added together. Assume that both vectors point from the center, outward. The length of the hour hand is 5.10 [cm]; while the length of the minute hand is 10.50 [cm].What should Hardy tell the dolphins if the current time is:A. 10:30 AM, in bearing form? B. 1:25 PM, in unit vector form?
A girl delivering newspapers covers her route by traveling 7.00 blocks west, 4.00 blocks north, and then 3.00 blocks east. (a) What is her resultant displacement?
A particle travelled 3.9 m north then turned west and travelled 9.5 m in that direction and lastly, travelled 3.9 m south. If instead the particle turned north and travelled 5.7 m for its third displacement and eventuallv turned west again and travelled 6.7 m, find the particle's total displacement during its journey.