Question

1. Assume an intercontinental ballistic missile goes from rest to a suborbital speed of 8.50 km/s in 70.0 s (the actual speed and time are classified). What is its average acceleration in meters per second and in multiples of g (9.80 m/s²)?
2. A particle moves in a straight line with an initial velocity of 35 m/s and constant acceleration 30 m/s². (a) What is its displacement at t = 8 s? (b) What is its velocity at this same time?
3. You throw a ball straight up with an initial velocity of 18.0 m/s. It passes a tree branch on the way up at a height of 6.0 m. How much additional time elapses before the ball passes the tree branch on the way back down?

Answer 1

1)

$$a=\frac{8500}{70}=121\frac{m}{s^2}\\a=12.4g$$

2) a)

$$s=35(8)+0.5(30)(8)^2=1240\ m$$

b)

$$v=35+30(8)=275\frac{m}{s}$$

3)

$$T=2\frac{v}{g}\\t=2\frac{2h}{v}\\\tau=T-t=2\frac{v}{g}-4\frac{h}{v} \\\tau=2\frac{18}{9.8}-4\frac{6}{18}=2.3\ s$$