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MATHalinoEngineering Math ReviewHorizontal Motion
If a mass of fluid moves horizontally along a straight line at constant acceleration a, the liquid surface assume an angle θ with the horizontal, see figure below.
Problem 1012
A train moving with constant acceleration travels 24 ft (7.32 m) during the 10th second of its motion and 18 ft (5.49 m) during the 12th second of its motion. Find its initial velocity and its constant acceleration.
Problem 1011
A ship being launched slides down the ways with constant acceleration. She takes 8 sec to slide (the first foot | 0.3048 meter). How long will she take to slide down the ways if their length is (625 ft | 190.5 m)?
Problem 1010
A stone is thrown vertically up from the ground with a velocity of 300 ft per sec (91.44 m/s). How long must one wait before dropping a second stone from the top of a 600-ft (182.88-m) tower if the two stones are to pass each other 200 ft (60.96 m) from the top of the tower?
Problem 1009
A ball is shot vertically into the air at a velocity of 193.2 ft per sec (58.9 m per sec). After 4 sec, another ball is shot vertically into the air. What initial velocity must the second ball have in order to meet the first ball 386.4 ft (117.8 m) from the ground?
Problem 1004
A ball is dropped from the top of a tower 80 ft (24.38 m) high at the same instant that a second ball is thrown upward from the ground with an initial velocity of 40 ft/sec (12.19 m/s). When and where do they pass, and with what relative velocity?
Problem 1002
On a certain stretch of track, trains run at 60 mph (96.56 kph). How far back of a stopped train should be a warning torpedo be placed to signal an oncoming train? Assume that the brakes are applied at once and retard the train at the uniform rate of 2 ft/sec2 (0.61 m/s2).
Motion of a Particle
Particle is a term used to denote an object of point size. A system of particles which formed into appreciable size is termed as body. These terms may apply equally to the same object. The earth for example may be assumed as a particle in comparison with its orbit, whereas to an observer on the earth, it is a body with appreciable size. In general, a particle is an object whose size is so small in comparison to the size of its path.
Rectilinear Translation (Motion Along a Straight Line)