A particle starts from the origin at t = 0 with a velocity of 7.8 and moves in the xy plane with a constant acceleration of (4.41 + 3.0)) m/s² .At the instant the particle's x coordinate is 29 m, what are (a) its y coordinate and (b) its speed? (a) Number (b) Number 48 i Units Units m m/s
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- the coordinates of an object moving in an xy plane vary with the time according to the eqations x=-7.85 sin w(omega)t, and y=4-7.85 cosw(omega)t. W(omega) is constant , x,y - in meters. And t in seconds. Write expressions for the possition,velocity and acceleration vectors of the object at any time t>0.(a) What is the magnitude of the vector (17î − 27) m/s?Vector A is in the direction 39 0° clockwise from the -y-axis. The T-component of A is A, = -12.0 m.
- 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/s2Current Attempt in Progress In reaching her destination, a backpacker walks with an average velocity of 1.41 m/s, due west. This average velocity results, because she hikes for 6.94 km with an average velocity of 2.42 m/s due west, turns around, and hikes with an average velocity of 0.638 m/s due east. How far east did she walk (in kilometers)? VW 71 Number i West Units dw VE East dEPart A) A projectile is launched with speed v0v0 and angle θθ. Derive an expression for the projectile's maximum height hh. Express your answer in terms of the variables v0v0, θθ, and appropriate constants. Part B) A baseball is hit with a speed of 34.0 m/sm/s . Calculate its height if it is hit at an angle of 30.0 ∘∘ . Express your answer with the appropriate units. Part C) A baseball is hit with a speed of 34.0 m/sm/s . Calculate its distance traveled if it is hit at an angle of 30.0 ∘∘ . Express your answer with the appropriate units. Part D A baseball is hit with a speed of 34.0 m/sm/s . Calculate its height if it is hit at an angle of 45.0 ∘∘ . Express your answer with the appropriate units. Part E) A baseball is hit with a speed of 34.0 m/sm/s . Calculate its distance traveled if it is hit at an angle of 45.0 ∘∘ . Express your answer with the appropriate units.
- 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.)According to Los Angeles Air Traffic Control, an Air Force SR-71 has a constant velocity of 1942 knots (999 m/s) along the negative y direction, and a Navy F-18 has an acceleration of 4 m/s^2 along the positive x direction (both of these are fighter jets). What is the acceleration of the F-18 as measured by an observer in the SR-71 (in m/s^2)? [i and j represent unit vectors along the x and y directions respectively]14. You are running north at 5.90ms. Let’s call you Jogger A. Jogger B is currently ahead of you and is also jogging north at 1.88ms. From your frame of reference, what is the speed and direction of Jogger B?Assume that north is in the positive direction and south is in the negative direction. −4.02ms −7.41ms −1.29ms −5.47ms None of these is correct.
- 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.An object located at ?⃗0 = (1, 1) ? is displaced by Δ?⃗01 = −2?̂ − 5?̂ ? The object is then displaced by Δ?⃗12 = 3?̂ + 2?̂ ? a) Draw a picture b) What is the final position (?⃗2) of the object? c) How far did the object travel during each displacement? (?: 5.39 ?; 3.61 ?) d) What is the total distance travelled by the object? (?: 9 ?) e) How far did the object end up from where it initially started?(?: 3.16?)