Question

A stone propelled from a catapult with a speed of 59meter per seconds attain a height of 100 meter calculate
a. the time of flight
b. the angle of the projection
c. the range attain

Answer 1

I guess you mean maximum height of 100 m
Vertical problem:
Vi = 59 sin A
v = Vi - 9.81 t
at top v = 0
0 = Vi - 9.81 t
so
t = 59 sin A /9.81 at top

100 = Vi t - (9.81/2) t^2
100 = (59 sinA)^2/ 9.81 -(9.81/2) (59 sin a)^2/9.81^2

100 = (1/2)(59 sin A)^2/9.81
980*2 = (59 sin A)^2
44.27 = 59 sin A
A = 48.6 degrees
The rest is easy
sin A = .75
cos A = .661
time rising = 59 (.75)/9.81
= 4.51
SO TOTAL flight time = 2 t = 9.02 seconds (PART A)
angle A = 48.6 degrees (PART B)
range = 59 cos A * 9.02
= 352 meters (PART C)

Answer 2

time of flight t =2* 2hg =2*2*100/10 =2* 200/10 =2* 20 =2*4.47 =8.945