Projectile motion of a cannon ball

AI Thread Summary
A cannonball is fired at a 40-degree angle, traveling 300 meters horizontally before hitting a cliff that is 10 meters higher than the cannon's position. The discussion involves calculating the initial velocity of the cannonball using projectile motion equations. The initial calculations suggest an initial velocity of approximately 42.71 m/s, but further verification indicates that the correct initial speed is 48.8 m/s. The calculations take into account both the horizontal and vertical components of motion, integrating to find time and position. The final consensus confirms the need for accurate calculations in projectile motion scenarios.
Ry122
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a ball is fired from a cannon at an angle of 40 degrees to the horizontal and it travels 300m before hitting the side of a cliff which is 10 meters higher than the cannons position.
Determine the initial velocity.

The ball has a negative velocity when it hits the cliff.

My attempt:
Where v = the balls initial velocity
y component of velocity = -9.81t + Vsin40

integrate this and get

y position = .5*-9.8t^2 + vsin40t

x component of velocity = vcos40

integrate this and get

x position = vcos40tUsing the expression for x velocity, solve for t at 300m in the x direction and get the expression
t=300/vcos40

Sub this into the expression for the y position above and solve for v.I'm unsure if this is the correct way to go about doing this. The velocity I ended up with is 42.7124ms^-1 which seems a bit slow for the distance it covers.
 
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Your method is correct.
I check your answer, but I got the initial speed is 48.8 m/s.
 
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