Next consider the case where the angle 0 is 40.2° and the penguin is sliding down the hill. Using Newton's Second Law of Motion, determine the acceleration of the penguin. Note that the solution for acceleration should be written in unit vector notation using the rotated coordinate system. Assume that the mass of the penguin is 5.11 kg and that g = 9.81 m/s?. Answer in units of m/s² with 3 sig figs.
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- A vector with magnitude 6, points in a direction counterclockwise from the positive x-axis. Write the vector in component form. Give each value accurate to at least 1 decimal place.A force F1 of magnitude 6.30 units acts on an object at the origin in a direction θ = 47.0° above the positive x-axis. (See the figure below.) A second force F2 of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Find graphically the magnitude and direction of the resultant force F1 + F2.= A polo ball is hit with a mallet off the edge of a cliff. Its x- and y-coordinates as functions of time are given by x = 16.8t and y meters and t is in seconds. (Do not include units in your answer.) (a) Write a vector expression for the ball's position as a function of time (in m), using the unit vectors î and ĵ. (Give the answer in terms of t.) r= 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 (c) Obtain the expression for the acceleration vector a as a function of time (in m/s²). m/s² II m/s to || (d) Next, use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the polo ball at t = 2.85 s. (Assume the position is in m, the velocity is in m/s and the acceleration is in m/s².) 3 3.72t - 4.90t2, where x and y are in m/s m/s²
- Two blocks are connected by a (massless) string that runs over a (massless, frictionless) pulley as shown. Assume there is no friction between block 1 and the surface of the incline. 40° 2 If m₁ = 3.9 kg and m₂ = 5.9 kg, what is the tension in the string? Express your answer in N, to at least one digit after the decimal point.A force F, of magnitude 5.70 units acts at the origin in a direction 40.0° above the positive x axis. A second force F, of magnitude 5.00 units acts at the origin in the direction of the positive y axis. Find graphically the magnitude and direction of the resultant force F, + F magnitude units direction counterclockwise from the +x axis Need Help? ReadProblem 4: Vector Addition. Vector A = 200 NZ45° counterclockwise from the z axis, and vector B = 300 N 270° counterclockwise from the y axis. Find the resultant R= A + B by addition of scalar components. Problem 5: Consider the picture below. Find the tension T, tension Ta tension T₂
- I do not know how to get started with my graph. Does my x axis need to be between 7.84 or 15.68 and my y axis between 0.779 or 1.558. If so how should I start my graph and how much should I go up by with both x and y axis's. Please help! I am confused.If a force, F, has a magnitude of 45 N and is at an angle of 65 degrees (relative to the x-axis) then what is the magnitude of the x and y components (Fx and Fy) of this force? Double check your result by calculating the total force and angle using Fx and Fy.The weight of one dozen apples is 4.3 lb. Determine the average mass of one apple in both SI and US units and the average weight of one apple in SI units. In the present case, how applicable is the "rule of thumb" that an average apple weighs 1 N? Answers: Mass of one apple = Mass of one apple = Weight of one apple = i i i kg slugs N
- The vector v has magnitude 13 and makes an angle of 285 degrees with the positive x-direction. Express v in terms of components, with i and j being unit vectors pointing in the x and y directions respectively. Give each component to 1 d.p.Workmen are trying to free an SUV stuck in the mud. To extricate the vehicle, they use three horizontal ropes, producing the force vectors shown in the figure.(Figure 1) Take F1 = 937 N, F2 = 793 N, and F3 = 326 NN. Find the x components of each of the three pulls. Express your answers in newtons separated by commas. Find the y components of each of the three pulls. Express your answers in newtons separated by commas. Use the components to find the magnitude of the resultant of the three pulls. Express your answer in newtons to three significant figures. Use the components to find the direction of the resultant of the three pulls. Express your answer in degrees as the angle counted from +x axis in the counterclockwise direction.