Problem 87.86 The figure shows an arcade game called skee ball that is
similar to bowling. The player rolls the ball down a horizontal alley.
The ball then rides up a curved lip and is launched at an initial
speedu, at an angleαabove horizontal. Suppose we want the ball
to go into a hole that is at horizontal distance`and heighth, as
shown in the figure.
(a) Find the initial speeduthat is required, in terms of the other
variables andg.
√(b) Check that your answer to part a has units that make sense.
(c) Check that your answer to part a depends ongin a way that
makes sense. This means that you should first determine on physical
grounds whether increasinggshould increaseu, or decrease it. Then
see whether your answer to part a has this mathematical behavior.
(d) Do the same for the dependence onh.
(e) Interpret your equation in the case whereα= 90◦.
(f) Interpret your equation in the case where tanα=h/`.
(g) Findunumerically ifh= 70 cm,`= 60 cm, andα= 65◦.√Problem 86.87 The figure shows the International Space Station (ISS). One of
the purposes of the ISS is supposed to be to carry out experiments in
microgravity. However, the following factor limits this application.
The ISS orbits the earth once every 92.6 minutes. It is desirable to
keep the same side of the station always oriented toward the earth,
which means that the station has to rotate with the same period.
In the photo, the direction of orbital motion is left or right on the
page, so the rotation is about the axis shown as up and down on the
page. The greatest distance of any pressurized compartment from
the axis of rotation is 36.5 meters. Find the acceleration due to the
rotation at this point, and the apparent weight of a 60 kg astronaut
at that location.
√Problems 241