The document shows a table with the height and time for freely falling bodies. It explains that to calculate the height, you multiply the square of time by half the acceleration due to gravity (1/2g). It then provides some shortcuts for calculating the height by rounding the acceleration due to gravity to 5 m/s^2 and subtracting a small amount based on the square of time. This allows for an easier calculation of height compared to using the exact value of 4.9 m/s^2.

1. amazing, shortcutsfor freelyfallingbodies
height Time (t seconds) Square of time(t2
:
seconds x seconds)
(1/2)g
4.9m 1s 1s2
4.9m/s2
19.6m 2s 4s2
4.9m/s2
44.1m 3s 9s2
4.9m/s2
78.4m 4s 16s2
4.9m/s2
122.5m 5s 25s2
4.9m/s2
176.4m 6s 36s2
4.9m/s2
240.1m 7s 49s2
4.9m/s2
313.6m 8s 64s2
4.9m/s2
To findthe heightof a freelyfallingbodywe multiplythe valuesinthe square of time byour(1/2)g ,thus
(1s2
)( 4.9m/s2
)=4.9m,
(4s2
)( 4.9m/s2
)=19.6m
(9s2
)( 4.9m/s2
)=44.1m
(16s2
)( 4.9m/s2
)=78.4m
shortcuts:
(1s2
)( 4.9m/s2
)=4.9m,can be (1s2
)( 5m/s2
)=5m-(0.1s2
)(1m/s2
)=5m-0.1m=4.9m
(4s2
)( 4.9m/s2
)=19.6m can be (4s2
)( 5m/s2
)=20m-(0.4s2
)(1m/s2
)=20m-0.4m=19.6m
(9s2
)( 4.9m/s2
)=44.1m can be (9s2
)( 5m/s2
)=45m-(0.0s2
)(1m/s2
)=45m-0.9m=44.1m
(16s2
)( 4.9m/s2
)=78.4m can be (16s2
)( 5m/s2
)=80m-(1.6s2
)(1m/s2
)=80m-1.6m=78.4m
hint:
for 1second1 x 5 -0.1= 4.9m
for 2seconds4 x 5 -0.4= 19.6m
for 3seconds9 x 5 -0.9= 44.1m
for 4seconds16 x 5 -1.6= 78.4m