A ball is thrown straight up from the edge of the roof of abuilding. A second ball is dropped from the roof 1.00 s later. Ignoreair resistance. (a) If the height of the building is 20.0 m, what must theinitial speed of the first ball be if both are to hit the ground at the sametime? On the same graph, sketch the positions of both balls as a functionof time, measured from when the first ball is thrown. Consider thesame situation, but now let the initial speed v0 of the first ball be givenand treat the height h of the building as an unknown. (b) What mustthe height of the building be for both balls to reach the ground at thesame time if (i) v0 is 6.0 m/s and (ii) v0 is 9.5 m/s ? (c) If v0 is greaterthan some value vmax, no value of h exists that allows both balls to hitthe ground at the same time. Solve for vmax. The value vmax has a simplephysical interpretation. What is it? (d) If v0 is less than some value vmin,no value of h exists that allows both balls to hit the ground at the sametime. Solve for vmin. The value vmin also has a simple physical interpretation.What is it?
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
A ball is thrown straight up from the edge of the roof of a
building. A second ball is dropped from the roof 1.00 s later. Ignore
air resistance. (a) If the height of the building is 20.0 m, what must the
initial speed of the first ball be if both are to hit the ground at the same
time? On the same graph, sketch the positions of both balls as a function
of time, measured from when the first ball is thrown. Consider the
same situation, but now let the initial speed v0 of the first ball be given
and treat the height h of the building as an unknown. (b) What must
the height of the building be for both balls to reach the ground at the
same time if (i) v0 is 6.0 m/s and (ii) v0 is 9.5 m/s ? (c) If v0 is greater
than some value vmax, no value of h exists that allows both balls to hit
the ground at the same time. Solve for vmax. The value vmax has a simple
physical interpretation. What is it? (d) If v0 is less than some value vmin,
no value of h exists that allows both balls to hit the ground at the same
time. Solve for vmin. The value vmin also has a simple physical interpretation.
What is it?
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