Question

In a hockey match a hockey ball is hit 18m from the front of the goal. The ball leaves the hockey stick with initial velocity v at angle theta to the horizontal ground. The ball passes over the goal at a maximum height of 2.0m.
The initial vertical component of the velocity of the ball is 6.3ms-1. Air resistance has negligible effect on the motion of the ball.
Show that the time take for t to reach maximum height is about 0.6s.

I used suvat and got
s-2
u-6.3
no v
a-9.81
t ??????
so s=ut + 1/2at^2 has to be used to find t. I kept trying to rearrange find the answer but couldn’t do please help using suvat!!!

Show that the time take for t to reach maximum height is about 0.6s.

Answer 1

I am calling initial speed s, not v. For me v is vertical component

vertical problem only
Vi = s sin theta
v = Vi - g t = Vi - 9.8 t
at top v = 0
0 = Vi - 9.8 t
so
9.8 t = s sin theta
t = (s/9.8) sin theta at top
now height h
h = 0 + Vi t -4.9 t^2
2 = Vi t - 4.9 t^2
4.9 t^2 - Vi t + 2 = 0
but we know Vi = 9.8 t
4.9 t^2 - 9.8 t^2 + 2 = 0
4.9 t^2 = 2
t = 0.64 seconds to top

now you can go back and find Vi which better be 6.3 and theta and u = 18/t and then tan theta = Vi/u