The coordinates of a particle moving along a curve are x(t) = -2t2 +15 and y(t) = t2 -10t + 15, m when t is in seconds. Calculate the magnitude of velocity and %3D %3D acceleration when t= 5 sec.
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- 1つ7 3. An object undergoes motion in 2 dimensions under a constant acceleration of "-2.50 m/s at an angle of 50.0° with respect to the + x direction. It also has an initial velocity of vi = 7.00 m/s at an angle of 10,0° The object begins at the coordinates (0, 0). a) What are the coordinates of the object at t = 7.00 s? Want Cx, y) at t =?4 4tzテメ0チ=XT vse this Con Vxi = \V;l cos v +ハ Ay=lalsin Ga b) What is its total velocity vector of the object as a magnitude and direction at t = 7.00 s? a) Ov= TonA man starts walking north at 4f t/s from a point P. Five minutes later a woman starts walking southat 5f t/s from a point 500f t due east of P. At what rate are the people moving apart 15m after the womanstarts walking.An object on a horizontal plane has an initial velocity Vo = (6.01+3.05)m/s at & point where its position vector is r = (12.01+6.05)m gin. The object moves with constant acceleration and after t=7 s, its velocity becomes V = (-8.0t - 4.05m/s. What is its position vector at O26-145 O20f-105 O22f+165 O 181+125 O24f+ 185
- Problem 2: A baseball is thrown with velocity vo at an angle 0 = 45° above the horizontal. The vertical component of the initial velocity is vo.y = 12.25 m/s. Use a Cartesian coordinate system with the origin at the baseball's initial position.In 1999, Robbie Knievel was the first to jump the Grand Canyon on a motorcycle. At a narrow part of the canyon (69.0 m wide) and traveling 35.8 m/s off the takeoff ramp, he reached the other side. What was his launch angle?Check Your Understanding Verify that vector v V obtained in Example 2.14 is indeed a unit vector by computing its magnitude. If the convoy in Example 2.8 was moving across a desert flatland—that is, it the third component of its velocity was zero—what is the unit vector of its direction of motion? Which geographic direction does it represent?
- A particle travels m a circular orbit of radius 10 m. Its speed is changing at a rate of 15.0m/s2 at an instant when its speed is 40.0 m/s. What is the magnitude of the acceleration of the particle?A small plane flies at 200 km/h in still air. If the wind blows directly out of the west at 50 km/h, (a) in what direction must the pilot head her plane to move directly north across land and (b) how long does it take her to reach a point 300 km directly north of her starting point?nments Question 2 ssions The acceleration vector is tangent to the hodograph. O True O False Dus omes zes Question 3
- The figure shows the path taken by a drunk skunk over level ground, from initial point i ta final point f. The angles are 0, - 31.0, 0, - 46.0, and 0, - 84,0, and the distances ared, - 5.20 m, d, - 7.10 m, and dy - 12.0 m. What are the (a) magnitude and (b) angle of the skunk's displacerment fromi to f? Give the angle as a pusitive (cuunterckockwise) ur nugative (clotkwise) angle of magnitude less than 180', measured from the +xdlirection. (a) Number Units (b) Number UnilsAn electron’s position is given by ,with t in seconds and in meters. (a) In unit-vector notation, whatis the electron’s velocity ? At t 2.00 s, what is (b) in unit-vector notation and as (c) a magnitude and (d) an angle relative tothe positive direction of the x axis?1110. In Fig. P-1109, a ball thrown down the incline strikes it at a distance s 254.5 It. If the ball rises to a maximum height h 64.4 ft above the point of release, compute its initial velocity vo and inclination 6. Ans. v. = 80.5 ft per see; 0= 53.1° FIG. P-1109 and P-1110.