(a) Find the position vector of a particle that has the given acceleration and the specified initial velocity and po a(t) = 19ti + etj + e-tk, v(0) = k, r(0) = j + k r(t) (b) On your own using a computer, graph the path of the particle.
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- Find the position vector of a particle that has the given acceleration and the specified initial velocity and position. Then on your own using a computer, graph the path of the particle. a(t) = 7ti + e'j + e*k, v(0) = k, r(0) = i+ k r(t) A projectile is fired with an initial speed of 190 m/s and angle of elevation 60°. (Use g = 9.8 m/s?. Round your answers to the nearest whole number.) (a) Find the range (in m) of the projectile. (b) Find the maximum height (in m) reached. m (c) Find the speed (in m/s) at impact. m/sBlocks A (mass 5.00 kg) and B (mass 6.50 kg) move on a frictionless, horizontal surface. Initially, block B is at rest and block A is moving toward it at 5.00 m/s. The blocks are equipped with ideal spring bumpers. The collision is head-on, so all motion before and after the collision is along a straight line. Let +x be the direction of the initial motion of block А. Part C Find the velocity of block B when the energy stored in the spring bumpers is maximum. Express your answer with the appropriate units. HÀ VB = Value Units Submit Request Answer Part D Find the velocity of block A after they have moved apart. Express your answer with the appropriate units. HÅ ? VĀ = Value UnitsAt time t = 0, a particle is located at the point (4,8,6). It travels in a straight line to the point (1,7,2), has speed 2 at (4,8,6) and constant acceleration - 3i -j- 4k. Find an equation for the position vector r(t) of the particle at time t.
- At time t=0, a particle is located at the point (3,9,4). It travels in a straight line to the point (7,8,6), has speed 6 at (3,9,4) and constant acceleration 4i-j+2k. Find an equation for the position vector r(t) of the particle at time t -O+¹+* The equation for the position vector r(t) of the particle at time t is r(t) = (Type exact answers, using radicals as needed.)At time t=0, a particle is located at the point (2,7,5). It travels in a straight line to the point (7,2,8), has speed 9 at (2,7,5) and constant acceleration 5i - 5j + 3k. Find an equation for the position vector r(t) of the particle at time t. ..... The equation for the position vector r(t) of the particle at time t is r(t) = ( ) i+ ( Dj+ ( D k.At time t = 0, a particle is located at the point (8,4,7). It travels in a straight line to the point (3,9,6), has speed 3 at (8,4,7) and constant acceleration negative 5i + 5 j - k. Find an equation for the position vector r(t) of the particle at time t.
- The position vector r describes the path of an object moving in space. Position Vector Time r(t) = 5ti + tj + 4 t = 2 (a) Find the velocity vector, speed, and acceleration vector of the object. v(t) = s(t) a(t) = (b) Evaluate the velocity vector and acceleration vector of the object at the given value of t. v(2) = a(2) =At time t= 0, a particle is located at the point (7,2,8). It travels in a straight line to the point (3,3,3), has speed 5 at (7,2,8) and constant acceleration - 4i +j-5k. Find an equation for the position vector r(t) of the particle at time t. The equation for the position vector r(t) of the particle at time t is r(t) = Di+ (Dj+ ) k. (Type exact answers, using radicals as needed.) Textbook Calculator Print Clear all Check answer 71°F Partly cloudyConsider a particle moving along a curve so that it is at position f(t) = (2+³, 2t²) at time t. Then the particle is moving parallel to (1, -2) at time t at the point when the direction of motion is =
- 4 Suppose the position vector of a particle in space at time t is given by: r = (12t,-312,-8t/2) (a) Find the particle's velocity and acceleration vectors. (b) Find the particle's speed and direction of motion.A model rocket is fired vertically upward from rest. Its acceleration for 60t, at which time the fuel is exhausted and it becomes a Exercise 2. the first three seconds is a(t) freely "falling" body. Fourteen seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to -8 ft/s in 5 s. The rocket then descend with constant velocity to the ground. a) Determine the position function s and the velocity function v (for all times t). b) At what time does the rocket reach its maximum height, and what is that height? c) At what time does the rocket land? a freely falling body experiences the gravitational acceleration g=-32 ft/s^2. You have 4 different stages. The corresponding accelerations are 1) 60t (accelerating for the first few seconds) 2) -32 (free falling body) 3) c, for some constant c (slowing down linearly) 4) 0, (constant velocity) piecewise function for a,v, and sThe position of a particle in the xy-plane at time t is r(t) = (t + 4) i+(²+2) j. Find an equation in x and y whose graph is the path of the particle. Then find the particle's velocity and acceleration vectors at t=4. The equation for the path of the particle is y=