amazing, shortcuts for freely falling bodies

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 find the height of a freely falling body we multiply the values in the square of time by our (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 1second 1 x 5 -0.1= 4.9m

for 2seconds 4 x 5 -0.4= 19.6m

for 3seconds 9 x 5 -0.9= 44.1m

for 4seconds 16 x 5 -1.6= 78.4m