Question

You desire to lay siege to a castle with fiery arrows. You can fire an arrows 13 m/s and you decide to attack by angling your shot 40 degrees above the horizontal as shown. You are 1.6 meters tall and the wall is 13 meters tall. Ignore air resistance. What is the furthest back you can stand and still hit the top of the castle wall? What maximum height does your arrow achieve?

Answer 1

max height the arrow reach can be determined by 3rd equation of motion

h = vy^2/ (2 g)

h = (13 sin 40)^2 / (2*9.8)

h = 4.787 m

max height the arrow can reach above ground

H = h + 1.6 = 6.387 m

so the arrow can't reach the top of the castle wall

======

Comment in case any doubt, will reply for sure.. Goodluck