I do not agree with your claim that range is maximised when launched at 45 degrees to the hill. The result of the problem suggests that the ideal launch angle is ##45 + \frac {\phi} {2}## away from the hill.
I have since worked out the solution to my own question, and have found that it is a...
I certainly think that there is some confusion here. I believe that the outline of the proof of the author is as such:
1. Consider the envelope of possible trajectories from a launch point.
2. When range is maximised, Vf is tangent to the envelope of possible trajectories. Because of this, Vf...
The question does ask for the angle of launch so as to maximise range, so it is definitely relevant. But why is it that for the trajectory that gives maximum range, its velocity upon landing is along the angle bisector of the hill and the vertical to the directrix?
I managed to solve this by tilting the axes along the hill, and calculating the range, and then differentiating wrt ##\theta## (angle launched from hill) to get the answer. However, I recently came across the alternative solution below:
The parabola it refers to represents the parabolic...
I get that:
##x(t) = A\cos(\omega t + \phi)##
##y(t) = A\sin(\omega t + \phi)## (from the above relevant equations). This agrees with the solution for part (a).
However, the solution manual claims in part (b) that:
In the case where ϕ1 = ϕ2 = 0 and A = B, the mass moves in a circle centered...
How did you know that acceleration's direction is constant in the above question?
And in that case, would it be correct to say that acceleration is constantly directed southeast (or 45 degrees south of east), despite the boy's direction changing? Why should that be so, if friction is supposed...
My guess was simply that as acceleration changes from the north to east direction, the total magnitude change of v is ##v \sqrt 2##.
Acceleration is ##\mu g##, so time would be ##\frac {v \sqrt 2} {\mu g}##. This agrees with the textbook solution.
What I do not understand is the trajectory...
Consider the equation
X (200, 50) + n (1, 0) -> Y (120, 30) + Z (70, 20) + 11 n(1, 0)
Let p be the mass of a proton, n be the mass of a neutron.
BE(X) = [50p + 150n - M(X)] c^2
BE(Y) = [30p + 90n - M(Y)] c^2
BE(Z) = [20p + 50n - M(Z)]c^2
The energy released when using BE (products) - BE...
If I am understanding correctly, you are suggesting that assuming the spring is not stretched much, it's inner circumference is L, which gives an outer perimeter length of (L + D*pi).
Are you suggesting that the tension is then kD*pi?
I am a little confused as to how such a tension translates...
Are you suggesting that the diameter of the semicircle is (D + 2L/pi)?
I think I need help with understanding how a vertical tension in the string even arises. It is obvious intuitively, but when I break the spring down into an infinitesimal element I cannot figure out why.
Considering the...
Which means that the leftward static friction force acts on the table cloth along the Horse/cloth interface?
By N3L, a rightward static friction acts on the horse?
Wld I be right to say that the object does move?
I ask this because this exam question seems to suggest that the Horse (analogous to the object) can somehow remain on the verge of slipping.
Sorry, I stated my question wrongly.
If we pushed the table (on the frictionless surface) such that it is on the verge of slipping, does the block on the table move?
Sorry, I stated my question wrongly.
If we pushed the table (on the frictionless surface) such that it is on the verge of slipping, does the block on the table move?