4. a 5.4 kg basketball approaches sally with a velocity of 6.5 m/s. sally bumps the ball, giving it a speed
of 7.7 m/s but in the opposite direction. what average force did she apply if the interaction time
between her hands and the ball was 0.15 seconds?

a). in this case, dh> 0 and sd> 0. if t becomes larger, the term "-tds" will become more negative. at some point, it is possible that -dts will be more negative than the dh is positive, and the reaction will become spontaneous. this is probably the correct answer, but you should look at all of the other possibilities and make sure of that.