- #1
Asdf123
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I need a bit of help with this simple question, it's not difficult at all but I just can't see what I did wrong. I'm overlooking a crucial thing
A cannon is placed 40m away from a 37.5m high cliff.
The cannon fires a ball with an angle of 45 degrees to the horizontal.
The gravitational acceleration is 10 m/s^2.
The question is: with what mininum initial speed must the ball be fired so that it just hits the top of the cliff?
I tried to split the velocity in two components, both vx and vy.
vx = v0x * t (since there is no net force in the x-direction)
vy = v0y - gt (the only force that acts on the ball is gravity)
Since the ball is at it's highest point it's velocity in the y direction must be equal to 0. In that case, v0y = gt, so
t = v0y/g = v0y/10.
I can substitute this time in the equation for the y- position of the ball and find what the initial speed must be to reach that height
Sy = v0y*t - 1/2 * g * t^2
= v0y*t - 5*t^2
since t = v0y/10, and sy must be equal to 37.5
37.5 = 5/100 * v0y^2, v0y = sqrt(750) = 27.39
So v0 = 27.39/sin (45) =38.73 m/s
However, my textbook gives as answer v0 = 80 m/s. What am I doing wrong?
A cannon is placed 40m away from a 37.5m high cliff.
The cannon fires a ball with an angle of 45 degrees to the horizontal.
The gravitational acceleration is 10 m/s^2.
The question is: with what mininum initial speed must the ball be fired so that it just hits the top of the cliff?
I tried to split the velocity in two components, both vx and vy.
vx = v0x * t (since there is no net force in the x-direction)
vy = v0y - gt (the only force that acts on the ball is gravity)
Since the ball is at it's highest point it's velocity in the y direction must be equal to 0. In that case, v0y = gt, so
t = v0y/g = v0y/10.
I can substitute this time in the equation for the y- position of the ball and find what the initial speed must be to reach that height
Sy = v0y*t - 1/2 * g * t^2
= v0y*t - 5*t^2
since t = v0y/10, and sy must be equal to 37.5
37.5 = 5/100 * v0y^2, v0y = sqrt(750) = 27.39
So v0 = 27.39/sin (45) =38.73 m/s
However, my textbook gives as answer v0 = 80 m/s. What am I doing wrong?