Question

a ball projected vertically upwards with a velocity 19.6/s² find the maximum height reached by the stone and the time taken to reach the maximum height given g 9.8m/s²

Answer 1

 

Here is an answer with the figure, to help you understand better:

u = 19.5 m/s

t = 5 sec

g = 9.8 m/s²

Total distance covered while going up = S

total distance covered while coming down = h+S

At topmost point

v = 0

v = u - gt

0 = 19.5 - 10 (9.8)

t = 2 sec (appx)

 

Now, 

 

The velocity of ball when it falls down a distance S after reaching topmost height (h+S) will be same as initial velocity (calculate yourself), and the time taken will again be 2 sec.

So, total time elapsed = time for going up S + time for coming down S = 2+2 = 4 sec

 

Total time = 5 sec

Remaining time = 5-4 = 1 sec

here u = 19.5 m/s(downwards) , t = 1 sec

h = ut + 1/2 g t²

h = 19.5 (1) + 1/2 (9.8) (1) = 19.5 + 4.9 = 24.4 m