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1.18 Elevator and falling marble*
At t - 0, an elevator departs from the ground with urf£orm speed.
At time T1 a child drops a marble through the floor. The marble
falls with uniform acceleration g = 9.8 m/s2, and hits the ground
T2 seconds later. Find the height of the elevator at time TI.
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1.19 Relative velocity*
By relative velocity we mean velocity with respect to a specified
coordinate system. (The term velocity-, alone, is understood to be
relative to the observer's coordinate system.)
(a) A point is observed to have velocity VA relative to coordinate system A. What is its vehicity relative to coordinate system B,
which is displaced from system A by distance R? (R can change
in time.)
(b) Particles a and b move in opposite directions around a circle
with angular speed ÿo, as shown. At t = 0 they are both at the point
r = lj, where l is the radius of tlle circle.
Find the velocity of a relative to b.
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1.20 Sportscar
A sportscar, Electro Fiasco I, can accelerate un2gormly to 100 km!h
in 3.5 s. Its maximum braking rate cannot exceed 0.7g. What is the
minimum time required to go 1.0 km, assuming it begins and ends
at rest?
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1.22 Jerk
The rate of change of acceleration is known as "jerk." Find the
direction and magnitude of jerk for a particle moving in a circle of
radius R at angular velocity ÿo. Draw a vector diagram showing the
instantaneous position, velocity, acceleration, and jerk.
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1.26 Range on a hilt*
An athlete stands at the peak of a hill that slopes downward unifolTnly at angle ¢. At what angle 0 from the horizontal should they
throw a rock so that it has the greatest range?
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