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PROBLEM NO. 5 The motion of two particles, A and B, is described by the position vectors, TA = [(3t)i + (9t(2-t)); ] and, rg = [(3(t²-2t + 2))i + (3(t-2))j] Find the point at which the particles collide and their speeds just before the collision.

PROBLEM NO. 5 The motion of two particles, A and B, is described by the position vectors, TA = [(3t)i + (9t(2-t)); ] and, rg = [(3(t²-2t + 2))i + (3(t-2))j] Find the point at which the particles collide and their speeds just before the collision.

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NOTE: problem 3:  assume that the coordinates (5,10) are in km problem 5: only put “units” for the unit of both speed
PROBLEM NO. 5 The motion of two particles, A and B, is described by the position vectors, TA = [(3t)i + (9t(2-t)); ] and, rg = [(3(t² - 2t + 2))i + (3(t - 2))j] Find the point at which the particles collide and their speeds just before the collision. PROBLEM NO.4 A particle travels along a path described by the parabola, y = 0.5x². The x-component of velocity is given by, vx = (7t)ft/s. When t = 0,x=y= 0. Find the particle's distance from the origin and the magnitude of its acceleration when, t = 1s. PROBLEM NO.3 A jet plane travels a vertical parabolic path defined by the equation, y = 0.4x². At point A with coordinates (5, 10), the jet has a speed of 250m/s, which is increasing at the rate of 0.8m/s². Calculate the magnitude of the jet's acceleration when it is at point A. PROBLEM NO. 2 Starting from rest, a cyclist travels around a horizontal circular path, p = 8m, at a speed, v = (0.075t² + 0.2t)m/s. Find the magnitude of her velocity and acceleration when she has traveled 3m. PROBLEM NO. 1 A ball is launched eastward from the ground at 30kph at 45 degrees angle from the ground. A shooter will shoot the ball at the peak of its trajectory. The shooter is 50m away from the plane of the ball's trajectory. The launch point of the ball is 20m west from the plane of trajectory's nearest point to the shooter. The gun's muzzle is 1.2m from the ground and the exit velocity of the bullet is 2736kph. Determine the angle the gun should be shot and the time after the ball's launch should the gun's trigger be pulled. Neglect trigger to bullet exit time and air friction.
Transcribed Image Text:PROBLEM NO. 5 The motion of two particles, A and B, is described by the position vectors, TA = [(3t)i + (9t(2-t)); ] and, rg = [(3(t² - 2t + 2))i + (3(t - 2))j] Find the point at which the particles collide and their speeds just before the collision. PROBLEM NO.4 A particle travels along a path described by the parabola, y = 0.5x². The x-component of velocity is given by, vx = (7t)ft/s. When t = 0,x=y= 0. Find the particle's distance from the origin and the magnitude of its acceleration when, t = 1s. PROBLEM NO.3 A jet plane travels a vertical parabolic path defined by the equation, y = 0.4x². At point A with coordinates (5, 10), the jet has a speed of 250m/s, which is increasing at the rate of 0.8m/s². Calculate the magnitude of the jet's acceleration when it is at point A. PROBLEM NO. 2 Starting from rest, a cyclist travels around a horizontal circular path, p = 8m, at a speed, v = (0.075t² + 0.2t)m/s. Find the magnitude of her velocity and acceleration when she has traveled 3m. PROBLEM NO. 1 A ball is launched eastward from the ground at 30kph at 45 degrees angle from the ground. A shooter will shoot the ball at the peak of its trajectory. The shooter is 50m away from the plane of the ball's trajectory. The launch point of the ball is 20m west from the plane of trajectory's nearest point to the shooter. The gun's muzzle is 1.2m from the ground and the exit velocity of the bullet is 2736kph. Determine the angle the gun should be shot and the time after the ball's launch should the gun's trigger be pulled. Neglect trigger to bullet exit time and air friction.
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