MULTIVARIABLE CALCULUS

1. [-/1 Points] DETAILS SCALCET9 13.4.001. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The table gives coordinates of a particle moving through space along a smooth curve. X 2.3 9,6 3.9 0.5 3.3 7.3 3.4 1.0 4.3 6.0 3.2 1.5 5.3 6.8 2.9 2.0 7.2 7.6 2.5 (a) Find the average velocities over the time intervals [0, 1], [0.5, 1], [1, 2], and [1, 1.5]. (Round your answers to one decimal place.) [0, 1] V ave [0.5, 1] Vave [1, 2] Vave [1, 1.5] Vave= (b) Estimate the velocity and speed of the particle at t = 1. (Use the time intervals [0.5, 1] and [1, 1.5] to calculate your answer. Round the speed to two decimal places.) v(1) = IV(1)| = Need Help? Read It Watch It2. [-/1 Points] DETAILS SCALCET9 13.4.005. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the velocity, acceleration, and speed of a particle with the given position function. r(t) = 7 cos(t) i + 6 sin(t) j v(t) = a(t) = IV(t)I = Sketch the path of the particle and draw the velocity and acceleration vectors for t = It y y 10 10 10 10 vl W17 5 5- 5 5 a al a a -10 10 -10 10 -10 -5 5 10 -10 - 5 5 10 - 5 - 5 - 5 - 5 O - 10 - 104 - 10 - 10 L Need Help? Read It Watch It3. [-/1 Points] DETAILS SCALCET9 13.4.011.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the velocity, acceleration, and speed of a particle with the given position function. r(t) = 4\\2ti + e*j + e-45k V(t) = a(t) = IV(t)I = Need Help? Read It Watch It Master It 4. [-/1 Points] DETAILS SCALCET9 13.4.017. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 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) = 10ti + sin(t) j + cos(2t) k, v(0) = i, r(0) = j r(t) = Need Help? Read It Watch ItDETAILS SCALCET9 13.4.019.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 5. [-/1 Points] The position function of a particle is given by r(t) = (t2, 5t, t2 - 16t). When is the speed a minimum? t = Need Help? Read It Watch It Master It 6. [-/1 Points] DETAILS SCALCET9 13.4.021. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A force with magnitude 25 N acts directly upward from the xy-plane on an object with mass 5 kg. The object starts at the origin with initial velocity v(0) = i - j. Find its position function and its speed at time t. r(t) = IV(t)1 = Need Help? Read It Watch It 7. [-/1 Points] DETAILS SCALCET9 13.4.023. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A projectile is fired with an initial speed of 240 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. m (b) Find the maximum height (in m) reached. m (c) Find the speed (in m/s) at impact. m/s Need Help? Read It Watch It8. [-/1 Points] DETAILS SCALCET9 13.4.025.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A ball is thrown at an angle of 450 to the ground. If the ball lands 88 m away, what was the initial speed of the ball? (Round your answer to the nearest whole number. Use g x 9.8 m/s.) Vo m/s Need Help? Read It Watch It Master It 9. [-/1 Points] DETAILS SCALCET9 13.4.034. MY NOTES ASK YOUR TEACHER Water traveling along a straight portion of a river normally flows fastest in the middle, and the speed slows to almost zero at the banks. Consider a long straight stretch of river flowing north, with parallel banks 40 m apart. If the maximum water speed is 3 m/s, we can use the sine function, f(x) = 3 sin 40 as a basic model for the rate of water flow x units from the west bank. Suppose a boater would like to pilot the boat to land at the point B on the east bank directly opposite point A. If the boat maintains a constant heading and a constant speed of 5 m/s, determine the angle (in degrees south of east) at which the boat should head. (Round your answer to one decimal place.) . south of east Need Help? Read It 10. [-/1 Points] DETAILS SCALCET9 13.4.040. MY NOTES ASK YOUR TEACHER Find the tangential and normal components of the acceleration vector. r(t) = ti + 2e'j + e25k at Need Help? Read It