your answer is correct time is 5 secs. but can you explain how
h is 126 +p and how t is 5 sec

can you please explain how h is 126+ p and how t is 5 secs

ya got it. thanks

for maximum/minimum points u can just let whatever is in the brackets = 0 and solve. in this case u had (t-5) thats why t=5

alternatively you can use the method of how MAXIMUM point is (-b/2a).

in this equation,
h = -5t^2 + 50t + p + 1
so a = -5, b = 50, c = p+1
(look at the coefficients. what comes before "t^2" will be your a, what comes before "t" will be your b and what is left will be your c. *take note of your positive & negative signs!)

so maximum point would be
-50 / 2(-5) = -50 / -10 = 5

hope this helps!

Thank you so much for the detailed explanation. understood nicely.