- #1
so_gr_lo
- 69
- 10
- Homework Statement
- Mechanics maths assignment.
Q.
A child is attempting to throw a ball over a wall of height 5m that is 12 m away. The ball is thrown at a speed of u ms^-1 from a height of 2m, at an angle theta to the horizontal. Assume g = 10 ms^-2.
i)
If the ball just clears the wall use the Cartesian equation of trajectory to find an expression for u^2 in terms of tan(theta).
ii)
Find u when theta = 45°
iii)
By differentiating a multiple of u^2 or otherwise, find the minimum speed at which the ball can be thrown in order for the wall to be cleared, and the angle at which it must be thrown.
I think I have the correct answers for the first two. I followed the method in this link https://www.youtube.com/watch?v=cZiA4U4QRZg for the last, using differentiation to find the min velocity, but the angle comes out very close to 45° like (ii), but the velocity is much lower. Think it may be because the question in the link has ball starting on the ground, whereas in the question above it is 3m above the ground. I inputted y = 5-2 = 3 into the Cartesian equation, maybe this is wrong? Or I have rearranged and differentiated the equation wrong.
Thanks
- Relevant Equations
- Cartesian equation of trajectory:
y = xtanθ - (gx[SUP]2[/SUP]sec[SUP]2[/SUP]θ)/2u[SUP]2[/SUP]
Attempt at solution in attachment.