The missile at P takes off at rest and rises vertically to Q in 10 s. It stops there because of some technical problems. If by some means, the missile is suddenly pointed 45 degrees and allowed to travel in free flight, determine the maximum height attained.

a. 3790 m
b. 3890 m
c. 3990 m
d. 3690 m

Let R be the maximum height the missile reaches
Let the height of Q from the ground be h_Q and the height of R be h_R.

h_Q = (1/2)a t² = 1280 m

v_Q = a t = 320 m/s as the missile starts from rest

v_Qy = 320 sin 45 = 226.27 m/s

v_Qy² = 2 g s
where s is the vertical distance between Q and R
s = 3202/(2 g) = 2610 m

h_R = h_Q + s = 3890 m

The maximum height attained by the missile is
3890 m.