The Rocket Travels Along A Straight Line With The Velocity: Mechanical Principles B - Dynamics Assignment, UC, New Zealand

Question 1

The Rocket travels along a straight line with the velocity changing with displacement as depicted by the graph shown in Fig. 1. Construct the s−t and a−s graphs. Also, determine the time required for the rocket to travel a distance s = 60 m if s₀= 0 when t = 0.

Question 2

The pitching machine throws the 0.5 kg ball towards the wall with an initial velocity V_A= 10 m/s at 30⁰ to the horizontal as shown. Calculate the velocity V_B1with which the ball will hit the wall at B. After striking the wall at B, the ball deflects backward at a velocity of V_B2 = 5.0 m/s at an angle of 20⁰ to the horizontal and follows the projectile path shown from B to C. Calculate the height h at which the ball is above point A in the return flight and the distance S at which it will hit the ground from the wall.

Two particles A and B are moving along two curvilinear paths as shown in Fig 3.  At the given instant, the tangential velocity and acceleration of the particle at A are 2.5 m/s and -0.3 m/s² respectively, and act upwards, as shown. Point A is at X_A = 8.0 m. At the same instant, particle B moving along the semi-circular path has velocity and acceleration equal to 2.0 m/s and 0.65 m/s², acting downwards, as shown in Fig. 3. Calculate the relative acceleration of particle B with respect to that of particle A at the instant given.

Question 4

Mass A is raised by moving the mass B towards the right, based on the rope and pulley arrangement shown in Fig. 4. When X_B =0, both blocks A and B will rest on the bottom surface with the free lengths of the rope on either side equal to 5 m as shown. The velocity of B varies as the function:

Calculate the velocity of mass A when the time t = 0.90 seconds. Neglect friction and masses of the rope and the pulleys.