1. A projectile travels in a tunnel with initial speed of 25 m/s. If the height of the tunnel is 5 m, find the maximum range of the projectile and the angle of velocity relative to the horizontal direction.
2. A car starts from rest with an acceleration of 1300 mi/h², which remains constant until its velocity reaches 65 mph. Thereafter, the car maintains this velocity. Determine the distance traveled by the car during the first 10 minutes.
3. For the first 8 seconds of motion the velocity of a particle in rectilinear motion is given by the equation $v = 7 - \frac{t^2}{10}$ where v is in m/s and t is in seconds. From t = 8s to t = 16s the motion of the particle is given by $a = \frac{t}{4} - 2$. If the initial position of the particle is s = 0 when t = 0, determine (a) the equations of the position, velocity and acceleration of the particle for each phase of motion; (b) and its position, velocity and acceleration when t = 4 s and when t = 12 seconds. (c) Also plot the s-t, v-t and a-t graphs for the motion during the interval from t = 0 to t = 16 s.
