# Projectile question — Cannonball fired over a hill

dyn
Homework Statement:
A 130m high hill is located halfway between the cannon and its target. If the cannonball is fired at an elevation angle of 30 degrees and just clears the hill to strike the target , calculate the initial velocity and the distance from the cannon to the target
Relevant Equations:
Time of flight , t= 2v sin(theta) /g where v is the initial speed and theta is the elevation angle
Time of flight is t = 2v sinθ /g = v/g for θ = π/6 so time to top of flight is t = v/(2g)

I then constructed a right-angle triangle with θ=π/6 and opposite side of 130m and used tangent to get the adjacent side , ie. distance from cannon to hill to be 225.17m
The horizontal velocity is v cosθ which is 0.866v. Using speed = distance /time I equated 0.866v to 225.17/ {v/(2g)} to get an equation for v squared which gives a final answer of v = 71.42 m/s and distance from cannon to target is 2 x 225.17 = 450.34 m

These are not the right answers but I have no idea why ?

Homework Helper
Gold Member
The mistake is here:
I then constructed a right-angle triangle with θ=π/6 and opposite side of 130m and used tangent to get the adjacent side , ie. distance from cannon to hill to be 225.17m
Make a sketch in which you draw the trajectory of the cannonball from the cannon to the top of the hill. (What is the shape of the trajectory?) Then draw a straight line from the cannon to the top of the hill. Does the straight line make a 30o angle to the horizontal?

• Lnewqban
dyn
Thanks for your reply. The trajectory is a parabola so I can't use the right angle triangle

• TSny
Homework Helper
Gold Member
Try this approach: you are told the highest vertical distance of the projectile. How long would it take to reach this height?

Homework Helper
Gold Member
Thanks for your reply. The trajectory is a parabola so I can't use the right angle triangle
What the initial velocity should be if the cannon is pointed perfectly vertical and you want the cannonball to reach the height of 130 meters only?
Then, if you tilt the cannon to an elevation angle of 30 degrees, trying to cover the horizontal distance to the target, still clearing the hill, should the initial velocity be greater than the one previously calculated for vertical shooting?
If so, how much it and its horizontal component should be?

dyn
Thanks everyone. I got it right now.

• Lnewqban