4. A particle is moving in the xy plane starting from the origin with an initial velocity in x of 15 meters per second and an initial velocity in y of – 10 meters per second. The object moves at constant velocity in x and constant acceleration in y. The acceleration in y is -1 m/s?. (a) Determine the total velocity vector v at any time, t. (Ans.: v7 = 15i – (10 + t)j ) (b) Determine the position of the particle ř at any time, t. (Ans.: * = (15t)i – (10t +t²) i ) What is the position of the particle after 5 seconds? (Ans.: r = 97.63 m, 0 = 39.81°)

4. A particle is moving in the xy plane starting from the origin with an initial velocity in x of 15 meters per second and an initial velocity in y of – 10 meters per second. The object moves at constant velocity in x and constant acceleration in y. The acceleration in y is -1 m/s?. (a) Determine the total velocity vector v at any time, t. (Ans.: v7 = 15i – (10 + t)j ) (b) Determine the position of the particle ř at any time, t. (Ans.: * = (15t)i – (10t +t²) i ) What is the position of the particle after 5 seconds? (Ans.: r = 97.63 m, 0 = 39.81°)

Name: 4. A particle is moving in the xy plane starting from the origin with
Uploaded: 2024-03-20T06:57:47.000Z
Channel: Bartleby
Description: 4. A particle is moving in the xy plane starting from the origin with an initial velocity in xof 15 meters per second and an initial velocity in y of – 10 meters per second. The objectmoves at constant velocity in x and constant acceleration in y. T

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

Chapter3: Motion In Two Dimensions

Section: Chapter Questions

Problem 3P: A particle initially located at the origin has an acceleration of a=3.00jm/s2 and an initial...

See similar textbooks

Similar questions

A fish swimming in a horizontal plane has velocity i = (4.00 î + 1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is i = (12.0 î − 2.60 ĵ) m. After the fish swims with constant acceleration for 15.0 s, its velocity is = (25.0 î − 1.00 ĵ) m/s. (a) What are the components of the acceleration of the fish? ax = ay = (b) What is the direction of its acceleration with respect to unit vector î? Draw coordinate axes on a separate piece of paper, and then add the acceleration vector with its tail at the origin. Write the numerical values for the x and y components and then use this drawing to determine the angle.° counterclockwise from the +x-axis(c) If the fish maintains constant acceleration, where is it at t = 28.0 s? x = m y = m In what direction is it moving? ° counterclockwise from the +x-axis
A snowmobile is originally at the point with position vector 29.0 m at 95.08 counterclockwise from the x axis, moving with velocity 4.50 m/s at 40.0 degrees. It moves with constant acceleration 1.90 m/s2 at 200 degrees. After 5.00 s have elapsed, find (a) its velocity and (b) its position vector.
A particle starts from the origin at t=0, with an initial velocity having an x component of 20m/s and a y component of -15m/s. The particle moves in the xy plane with an x component of acceleration only, given by Ax =4.0 m/s^2 Determine the components of the velocity vector at anytime and the total velocity vector at any time . Calculate the velocity and speed of the particle at t=5.0s.
A skater is gliding along the ice at 2.2 m/s, when she undergoes an acceleration of magnitude 1.2 m/s2 for 3.0 s. At the end of that time she is moving at 5.8 m/s. (a) What must be the angle between the acceleration vector and the initial velocity vector?
The velocity v→ of a particle moving in the xy plane is given by v→=(5.50t-5.00t2)î+9.00ĵ, with v→ in meters per second and t (> 0) in seconds. At t = 1.40 s and in unit-vector notation, At what positive time does the speed equal 10.0 m/s?
A particle initially located at the origin has an acceleration of a=3.00jm/s2 and an initial velocity of vi=5.00im/s. Find (a) the vector position of the particle at any time t, (b) the velocity of the particle at any time t, (c) the coordinates of the particle at t = 2.00 s, and (d) the speed of the particle at t = 2.00 s.
A hiker walks from (x1, y1) = (4.00 km. 3.00 km) to (x2, y2) = (3.00 km, 6.00 km), (a) What distance has the traveled? (b) The hiker desires to return to his starting point. In what direction should he go? (Give the angle with respect to due cast.) (See Sections 3.2 and 3.3.)
A squirrel is launched due west from a height of 10 meters with an initial velocity of 80 meters per second atan angle of 60 degrees above horizontal. A strong wind blowing directly out of the north causes the squirrel toaccelerate south at a rate of 2 m/s^2. All of this takes place in my backyard where acceleration due to gravity is 7 m/s2 (a) With the positive y–axis oriented north, the positive x–axis oriented east, and the positive z–axis up into the sky, findthe vector equation for the path of the squirrel. (b) Find the time when the squirrel is at her maximum height.
A fish swimming in a horizontal plane has velocity i = (4.00 î + 1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is i = (16.0 î − 3.20 ĵ) m. After the fish swims with constant acceleration for 15.0 s, its velocity is = (21.0 î − 6.00 ĵ) m/s. (a) What are the components of the acceleration of the fish? ax = m/s2 ay = m/s2 (b) What is the direction of its acceleration with respect to unit vector î? ° counterclockwise from the +x-axis(c) If the fish maintains constant acceleration, where is it at t = 30.0 s? x = m y = m In what direction is it moving? ° counterclockwise from the +x-axis
A fish swimming in a horizontal plane has velocity i = (4.00 î + 1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is i = (16.0 î − 3.20 ĵ) m. After the fish swims with constant acceleration for 15.0 s, its velocity is = (21.0 î − 6.00 ĵ) m/s. (a) What are the components of the acceleration of the fish? ax = m/s2 ay = m/s2 (b) What is the direction of its acceleration with respect to unit vector î? ° counterclockwise from the +x-axis(c) If the fish maintains constant acceleration, where is it at t = 30.0 s? x = 542.5 Remember that you can treat the motions in the x and y directions separately. Each is then treated exactly as you would the one-dimensional case. m y = m In what direction is it moving? ° counterclockwise from the +x-axi
A particle initially located at the origin has an acceleration of = 2.00ĵ m/s2 and an initial velocity of i = 9.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds).( t î + t2 ĵ) m(b) Find the velocity of the particle at any time t.( î + t ĵ) m/s(c) Find the coordinates of the particle at t = 3.00 s.x = my = m(d) Find the speed of the particle at t = 3.00 s. m/s
The positionr→of a particle moving in an xy plane is given byr→=(5.00t3−6.00t)i^+(2.00−2.00t4)j^withr→in meters and t in seconds. In unit-vector notation, calculate(a)r→, (b)v→, and (c)a→for t = 2.00 s. (d) What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t = 2.00 s? Give your answer in the range of (-180o; 180o).