4. The position 7 of a particle moving in an xy plane is given by 7 = (3t³-5t)i + (8t² - 12t^)j, with 7 in meters and t

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4 The Position 7 Of A Particle Moving In An Xy Plane Is Given By 7 3t 5t I 8t 12t J With 7 In Meters And T 1 (41.19 KiB) Viewed 37 times

4. The position 7 of a particle moving in an xy plane is given by 7 = (3t³-5t)i + (8t² - 12t^)j, with 7 in meters and t in seconds. In unit vector notation, calculate (a) Velocity (b) Acceleration for t = 4 s. (c) What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t = 4 s. [5] 5. You are to launch a rocket, from just above the ground, with one of the following initial velocity vectors: (i) = (38)i + (52)ĵ, (ii) = (38)i- (52)j. (iii)-(38)i-(52)j. (iv) = -(38)i + (52)). In your coordinate system, x runs along level ground and y increases upward. (a) Rank the vectors according to the launch speed of the projectile, greatest first. (b) Rank the vectors according to the time of flight of the projectile, greatest first. [5] 6. A ball is shot from the ground into the air. At a height of 10 m, its velocity is = (4.8)i + (12)jms ¹, with i horizontal and ĵ upward. Now solve the given questions- (a) To what maximum height does the ball rise? (b) What total horizontal distance does the ball travel? (c) What are the magnitude and angle of the ball's velocity just before it hits the ground?