Two rockets are launched at a fireworks display. Rocket A is launched with an initial velocity vo = 100 m/s and rocket B is launched t₁ sec- onds later with the same initial velocity. The two rockets are timed to explode simultaneously at a height of 300 m as A is falling and B is ris- ing. Assuming a constant acceleration g = 9.81 m/s², determine (a) the time t₁, (b) the velocity of B relative to A at the time of the explosion.

1. The curvilinear motion of a particle is defined by v, = 50- 16t and y = 100 – 4t2 where vz is velocity in meters per second and t, time in seconds. It is also known that x = 0 when t = 0. Determine the velocity and acceleration of the particle when position y = O is reached.

8. An application to mecanics A particule r(t) of mass 1kg is moving along an horizontal straight line (positively oriented on the right). The particle is under the effect of a positive constant force F(t) = g. Knowing that the particle what initially at the origin, with negative speed -vo, find the expression of x(t) time t in terms of g and vo and find the position further on the left where the particule will be. Finally, find the expression of the time T when the particle will be back at the origin.