#2 #6 #12 #142. What is the change in velocity for each of the following initial and final velocities?
a) 80 km/hr forward to 120 km/hr forward.
b) 80 km/hr forward to 120 km/hr backward.
6. A 60 kg person on a merry-go-round is traveling in a circle of radius 2 m at a speed of 4 m/s.
a) What acceleration does the person experience?
![The centripetal acceleration, a = (v^2)/r = [(4 m/s)^2]/(2 m) = 8 m/(s^2).](images/ch3x06a.gif)
b) What is the centripetal force? How does it compare with the person's weight?
![The centripetal force is the person's mass times the centripetal acceleration. F = (60 kg)[8 m/(s^2)] = 480 N. The person's weight is W = mg = (60kg)(10 m/s/s) = 600 N.](images/ch3x06b.gif)
12. A car drives off a vertical cliff at a speed of 20 m/s (45 mi/hr). If it takes 4 s for it to hit the ground, how far from the base of the cliff does it land?
This distance is the product of the horizontal velocity and the time of flight. Since there is no horizontal force (gravity is vertical), the horizontal velocity is 20 m/s throughout the trajectory. The distance the car lands from the base of the cliff is given by,
14. If a baseball is hit with a vertical speed of 20 m/s and a horizontal speed of 8 m/s, how long will the ball remain in the air. How far will it go?
To determine the horizontal distance the ball travels we want to multiply the horizontal speed by the time of flight. We find the time of flight by looking at the vertical motion.
Initially the ball has a vertical velocity of 20 m/s UP. At one second, the ball's velocity is 10 m/s UP. The ball is at its highest point at two seconds when its vertical velocity is zero. It takes two seconds to complete the first half of the trajectory, so the time of flight is twice this two seconds, for four seconds total time of flight.
Algebraic formula to find time of flight.Using this, we multiply by the baseball's constant horizonal velocity to find the horizontal distance the ball travels.
