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# Vertical Motion Example Problem – Coin Toss Equations of Motion

This equations of motion under constant acceleration exercise problem shows how to determine the utmost height, speed and time of escape for a mint flipped into a well. This problem could be modified to solve any object tossed vertically or dropped off a grandiloquent construction or any height. This type of problem is a common equations of motion homework problem. Problem:
A female child flips a coin into a 50 megabyte bass wish well. If she flips the coin upwards with an initial speed of 5 m/s :
a ) How high does the coin rise ?
boron ) How long does it take to get to this point ?
vitamin c ) How long does it take for the mint to reach the bottom of the well ?
five hundred ) What is the speed when the coin hits the bottom of the well ? Solution:
I have chosen the coordinate system to begin at the launch point. The maximum altitude will be at bespeak +y and the bottom of the well is at -50 m. The initial speed at launch is +5 m/s and the acceleration due to gravity is peer to -9.8 m/s2. The equations we need for this problem are :

1 ) yttrium = y0 + v0t + ½at2 2 ) volt = v0 + at 3 ) v2 = v02 + 2a ( yttrium – y0 ) Part a) How high does the mint originate ? At the top of the coin ’ randomness flight, the speed will equal zero. With this information, we have enough to use equation 3 from above to find the position at the crown. v2 = v02 – 2a ( yttrium – y0 )
0 = ( 5 m/s ) 2 + 2 ( -9.8 m/s2 ) ( y – 0 )
0 = 25 m2/s2 – ( 19.6 m/s2 ) yttrium
( 19.6 m/s2 ) yttrium = 25 m2/s2
y = 1.28 megabyte Part b) How retentive does it take to reach the top ? equality 2 is the utilitarian equation for this character. five = v0 + at
0 = 5 m/s + ( -9.8 m/s2 ) triiodothyronine
( 9.8 m/s2 ) thymine = 5 m/s
thymine = 0.51 sulfur Part c) How long does it take to reach the bottom of the well ? equation 1 is the one to use for this character. Set y = -50 thousand.

y = y0 + v0t + ½at2
-50 m = 0 + ( 5 m/s ) deoxythymidine monophosphate + ½ ( -9.8 m/s2 ) t2
0 = ( -4.9 m/s2 ) t2 + ( 5 m/s ) deoxythymidine monophosphate + 50 megabyte This equality has two solutions. Use the quadratic equation to find them.
where
a = -4.9
b = 5
c = 50 wherea = -4.9b = 5c = 50

t = 3.7 s or t = -2.7 s metric ton = 3.7 s or triiodothyronine = -2.7 s The negative time implies a solution before the coin was tossed. The fourth dimension that fits the situation is the incontrovertible respect. The fourth dimension to the bottom of the well was 3.7 seconds after being tossed. Part d) What was the speed of the coin at the penetrate of the well ? equality 2 will help here since we know the time it took to get there. v = v0 + at
v = 5 m/s + ( -9.8 m/s2 ) ( 3.7 s )
volt = 5 m/s – 36.3 m/s
five = -31.3 m/s The speed of the coin at the bottom of the well was 31.3 m/s. The negative sign of the zodiac means the guidance was down.

If you need more work examples like this one, check out these other constant acceleration case problems.
Equations of Motion – Constant Acceleration Example Problem
Equations of Motion – Interception Example Problem
Projectile Motion Example Problem

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