Cram University

Calc 3 10.9

<== Calculus 3
 Number Question Answer See the work 1. Find the velocity, acceleration, and speed of a particle with position function v(t) = &lang,, &rang a(t) = &lang,, &rang | v(t) | = v(t) = &lang , , 16t &rang a(t) = &lang,,16&rang | v(t) | = The work 2. Find the velocity and position vectors of a particle with acceleration a(t) = &lang 0,0,4 &rang, and initial conditions v(0) = &lang 3, -3, -5 &rang and r(0) = &lang 3, -2, -3 &rang . v(t) = &lang, , &rang r(t) = &lang, ,&rang v(t) = &lang 3, -3, 4t-5 &rang r(t) = &lang 3t+3, -3t-2, &rang The work 3. Given that the acceleration vector is a(t) = ( -cos(t) )i - ( sin(t) )j + (2t)k, the initial velocity is v(0) = i + k, and the initial position vector is r(0) = i + j + k, compute: A. The velocity vector v(t) = i + j + k B. The position vector r(t) = i + j + k v(t) = (-sin(t) + 1)i + (cos(t ) - 1)j + k r(t) = (cos( t ) + t)i + (sin( t ) -t + 1)j + ()k The work 4. The position function of a particle is given by . At what time is the speed minimum? -0.5 The work 5. A dense particle with mass 7 kg follows the path with units in meters and seconds. What force acts on the mass at t = 0? (, , ) kg*m/s^2 ( 0, -448, 0) kg*m/s^2 The work 6. A projectile is fired from ground level with an initial speed of 550 m/sec and an angle of elevation of 30 degrees. Use that the acceleration due to gravity is 9.8 . The range of the projectile is meters. The maximum height of the projectile is meters. The speed with which the projectile hits the ground is m/sec. Range of projectile = 26731.91 meters. Max height of projectile = 3858.42 meters. Speed projectile hits ground = 550 m/sec. The work 7. A ball is thrown at an angle of 45 degrees to the ground, and lands 40 meters away. The initial speed of the ball was m/sec. 19.799 m/sec The work 8. A body of mass 10 kg moves in a (counterclockwise) circular path of radius 8 meters, making one revolution every 12 seconds. You may assume the circle is in the xy-plane, and so you may ignore the third component. A. Compute the centripetal force acting on the body. (,) B. Compute the magnitude of that force. A) (-21.932cos(0.5236t), -21.932sin(0.5235t)) B) 21.932 The work