3-3

If writing process is bothering you,

it's ok to write only correct answer in each question.

1. Consider a particle with position function 7 (t) = (t2 + t, 3t, 2 Int). Find the velocity of the particle when it is at the point (2, 3, 0). Enter your answer as a combination of the basis vectors i , ] , #- For example, the vector (2, 3, 4) would be entered as 2*i+3*j+4*k. Preview will appear here... Enter math expression here 2. As in the previous question, consider a particle with position function r (t) = (t? + t, 3t, 2 In t)- Find the acceleration of the particle when it is at the point (2, 3, 0). Enter your answer as a combination of the basis vectors i , j , k . For example, the vector (2, 3, 4) would be entered as 2*i+3*j+4*k. Preview will appear here... Enter math expression here A particle moves through space, with its acceleration at time t given by a (t) = i + 3t j + 6t? k. The particle's initial velocity is V (0) = (1, 0, 4) and its initial position is 7(0) = (0, -2,3). Find the velocity vector for the particle at time t. O V(t) = (1, 3t, 2+3 + 4) O T(t) = ( t+ 1, 2+2, 2+3 + 4) O V(t) = (0, 3, 12t + 4) O v (t) = (t + 1, +3, 2+3 + 4) 4. As in the previous question, a particle moves through space, with its acceleration at time t given by d (t) = i + 3t j + 612 k. The particle's initial velocity is (0) = (1, 0, 4) and its initial position is T (0) = (0, -2,3). Find the position of the particle at time t. O T (t) = 2 + 1 , 3 10 - 2 , + + 41 + 3) 0 7() = (41+ t, 2+3 - 2, 4+ + at+3) 7(1) = (#+ + 1, 2+3 - 2, +4 + 41+3) O T(t) = (0, -2, 3) 5. True or false? If a particle moves at a constant speed, then its velocity and acceleration vectors are orthogonal (perpendicular). O True False6. If a particle has mass in and position function 7(#) = (cost, sin(2t), #2), what force acts on the particle at t = 0? Enter your answer as a combination of the basis vectors i , j , K . For example, the vector (2, 3, 4) would be entered as 2*i+3*j+4*k. Preview will appear here... Enter math expression here 7. A particle's position is given by r'(t) = (t?, 3t, 12 - 16t). At what time is its speed a minimum? Enter answer here 8. If a projectile is fired with angle of elevation & and initial speed vo. Assuming that the only external force is due to gravity, the position of the projectile can be modeled by a vector function in the plane, T' (t) = ((v, cos @)t, (vo sin 8)t - 2gt2), where g = 9.8 m/s" is the acceleration due to gravity. What angle of elevation maximizes the distance between the point from which the projectile is fired and the point where it hits the ground? Preview will appear here... Enter math expression here 9. A cannonball is fired at an initial speed of 100 m/s and angle of elevation 60". Find the maximum height reached by the cannonball. Round your answer to the nearest meter. Remember that projectile is fired with angle of elevation # and initial speed up has position function P (t) = ((un cos #)t, (vo sin #)t - 2gt?), where g = 9.8 m/s' is the acceleration due to gravity. Enter answer here 10. As before, a cannonball is fired at an initial speed of 100 m/s and angle of elevation 60". Find the cannonball's speed when it hits the ground. Round your answer to the nearest meter per second. Remember that projectile is fired with angle of elevation o and initial speed Up has position function F (t) = ((Uq cos #)t, (up sin #)t - Egt?), where g = 9.8 m/s" is the acceleration due to gravity. Enter answer here