Solved Problems In Engineering Dynamics 255l3z
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Problem 1002Problem 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). Solution HideClick here to show or hide the solution§English System Initial velocity
answer SI units Initial velocity
answer Problem 1003 A stone is thrown vertically upward and return to earth in 10 sec. What was its initial velocity and how high did it go? Solution HideClick here to show or hide the solution§Return in 10 seconds = 5 seconds upward + 5 seconds downward SI Units
Going upward (velocity at the highest point is zero): answer Going downward (initial velocity is zero; free-fall):
answer
English System Going upward (velocity at the highest point is zero): answer Going downward (initial velocity is zero; free-fall):
answer 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 , and with what relative velocity? Solution in English System HideClick here to show or hide the solution§h = 80 ft vA = 0 vB = 40 ft/s g = 32.2 ft/s2 From A to C (free-fall)
From B to C (upward motion) From the formula s = vit + ½ at2
A to C plus B to C is equal to height of the tower
They each other after 2 seconds at 64.4 ft from the top of the tower.
answer
Velocity at C of stone from A (after 2 seconds)
Velocity at C of stone from B (after 2 seconds) → the negative sign indicates that the stone is moving downward Relative velocity: answer
Problem 1005 A stone is dropped down a well and 5 sec later, the sounds of the splash is heard. If the velocity of sound is 1120 ft/sec (341.376 m/s), what is the depth of the well? Solution HideClick here to show or hide the solution§ For tstone (free-falling body):
For tsound (uniform motion):
Thus,
English System
For h = 88 759.73 ft (not okay!) For h = 353.31 ft (okay!) Thus, h = 353.31 ft
→ answer
SI Units
For h = 27 065.05 m (not okay!) For h = 107.64 m (okay!) Thus, h = 107.64 m
→ answer
Problem 1007 A stone is dropped from a captive balloon at an elevation of 1000 ft (304.8 m). Two seconds later another stone is thrown vertically upward from the ground with a velocity of 248 ft/s (75.6 m/s). If g = 32 ft/s2 (9.75 m/s2), when and where the stones each other? Solution in English Units Stone dropped from captive balloon (free-falling body):
Stone thrown vertically from the ground 2 seconds later The stones will each other 5 seconds after the first stone was dropped from the captive balloon. answer The stones will meet at a point 600 ft above the ground.
Answer
Problem 1008 A stone is thrown vertically upward from the ground with a velocity of 48.3 ft per sec (14.72 m per sec). One second later another stone is thrown vertically upward with a velocity of 96.6 ft per sec (29.44 m per sec). How far above the ground will the stones be at the same level? Solution in English System HideClick here to show or hide the solution§
For the first stone:
For the second stone
answer 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? Solution: English System of Units
Thus,
First ball:
Use Second ball:
answer
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 each other 200 ft (60.96 m) from the top of the tower? English System Solution Stone from the ground:
Stone from the top of the tower: Let t2 = time to wait before dropping the second stone With t = 17.19 sec
With t = 1.44 sec (meaningless) Use
answer
Problem 1012 A train moving with constant acceleration travels 24 ft (7.32 m) during the 10th sec of its motion and 18 ft (5.49 m) during the 12th sec of its motion. Find its initial velocity and its constant acceleration. Solution in English Units HideClick here to show or hide the solution§ → equation (1) → equation (2) Equation (1) minus equation (2) answer From equation (1)
answer
answer SI units Initial velocity
answer Problem 1003 A stone is thrown vertically upward and return to earth in 10 sec. What was its initial velocity and how high did it go? Solution HideClick here to show or hide the solution§Return in 10 seconds = 5 seconds upward + 5 seconds downward SI Units
Going upward (velocity at the highest point is zero): answer Going downward (initial velocity is zero; free-fall):
answer
English System Going upward (velocity at the highest point is zero): answer Going downward (initial velocity is zero; free-fall):
answer 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 , and with what relative velocity? Solution in English System HideClick here to show or hide the solution§h = 80 ft vA = 0 vB = 40 ft/s g = 32.2 ft/s2 From A to C (free-fall)
From B to C (upward motion) From the formula s = vit + ½ at2
A to C plus B to C is equal to height of the tower
They each other after 2 seconds at 64.4 ft from the top of the tower.
answer
Velocity at C of stone from A (after 2 seconds)
Velocity at C of stone from B (after 2 seconds) → the negative sign indicates that the stone is moving downward Relative velocity: answer
Problem 1005 A stone is dropped down a well and 5 sec later, the sounds of the splash is heard. If the velocity of sound is 1120 ft/sec (341.376 m/s), what is the depth of the well? Solution HideClick here to show or hide the solution§ For tstone (free-falling body):
For tsound (uniform motion):
Thus,
English System
For h = 88 759.73 ft (not okay!) For h = 353.31 ft (okay!) Thus, h = 353.31 ft
→ answer
SI Units
For h = 27 065.05 m (not okay!) For h = 107.64 m (okay!) Thus, h = 107.64 m
→ answer
Problem 1007 A stone is dropped from a captive balloon at an elevation of 1000 ft (304.8 m). Two seconds later another stone is thrown vertically upward from the ground with a velocity of 248 ft/s (75.6 m/s). If g = 32 ft/s2 (9.75 m/s2), when and where the stones each other? Solution in English Units Stone dropped from captive balloon (free-falling body):
Stone thrown vertically from the ground 2 seconds later The stones will each other 5 seconds after the first stone was dropped from the captive balloon. answer The stones will meet at a point 600 ft above the ground.
Answer
Problem 1008 A stone is thrown vertically upward from the ground with a velocity of 48.3 ft per sec (14.72 m per sec). One second later another stone is thrown vertically upward with a velocity of 96.6 ft per sec (29.44 m per sec). How far above the ground will the stones be at the same level? Solution in English System HideClick here to show or hide the solution§
For the first stone:
For the second stone
answer 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? Solution: English System of Units
Thus,
First ball:
Use Second ball:
answer
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 each other 200 ft (60.96 m) from the top of the tower? English System Solution Stone from the ground:
Stone from the top of the tower: Let t2 = time to wait before dropping the second stone With t = 17.19 sec
With t = 1.44 sec (meaningless) Use
answer
Problem 1012 A train moving with constant acceleration travels 24 ft (7.32 m) during the 10th sec of its motion and 18 ft (5.49 m) during the 12th sec of its motion. Find its initial velocity and its constant acceleration. Solution in English Units HideClick here to show or hide the solution§ → equation (1) → equation (2) Equation (1) minus equation (2) answer From equation (1)
answer
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