In Chapter 1, we presented a model for the vertical position s of an object that is launched straight upward with an initial velocity v₀ and initial position s₀: s = -1 /2 gt² + v₀t + s₀

Recall that t is the time after launch and g is the acceleration due to gravity.

1. A circus juggler tosses a ball straight upward from an initial height of 2.8 m with an initial velocity of 14.7 m/sec. If the acceleration due to gravity is 9.8 m/sec2 , write an equation representing the height of the ball t seconds after release _____________.

2. Complete the table to determine the height of the ball for the given values of t. Round to 1 decimal place. t (seconds) 0 , 0.5 ,1.0 , 1.5 , 2.0 , 2.5 , 3.0

h (meters)

3. Use the equation from question 1 to determine how long will it take the ball to return to the jugglers hand. ___________

4. Suppose that the juggler misses the ball and it falls straight to the ground instead of being caught. Determine the amount of time that the ball was in the air. Round to the nearest tenth of a second _______________.

5. There are two solutions to the quadratic equation in question 4. Discuss why the negative value was discarded. Also, discuss restrictions that should be placed on t, so that model breakdown does not occur.

6. Suppose that the time required for the ball to reach its maximum height is given by t_max = v₀ / g . Find the time for the ball to reach its maximum height. Compare the answer to the result from question 3.

7. Find the maximum height of the ball.