The height of a ball is thrown straight up sith a certain force is a function of the time (t) from which it is released given by f(t)=-0.5gt2+40t (where g is a constant determined by gravity). a. How does the value of t at which the height of the ball is at a maximum depend on the parameter g? b. Use your answer to part (a) to describe how maximum height changes as the parameter g changes. c. Use the envelope theorem to answer pare (b) directly. d. On the Earth g=32, but this value varies somewhat around the globe. If two locations had gravitational constants that differed by 0.1, what would be the difference in the maximum height of a ball tossed in the two places?
The height of a ball is thrown straight up sith a certain force is a function of the time (t) from which it is released given by f(t)=-0.5gt2+40t (where g is a constant determined by gravity).
a. How does the value of t at which the height of the ball is at a maximum depend on the parameter g?
b. Use your answer to part (a) to describe how maximum height changes as the parameter g changes.
c. Use the envelope theorem to answer pare (b) directly.
d. On the Earth g=32, but this value varies somewhat around the globe. If two locations had gravitational constants that differed by 0.1, what would be the difference in the maximum height of a ball tossed in the two places?
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