- #1

a1234

- 78

- 6

- Homework Statement
- I am given a problem where a 6kg object is launched from a cannon from an unknown initial height and eventually lands on top of a platform that is at a height of 40 meters above the ground. As you can see from the diagram, the final height is greater than the initial height.

The total displacement in the x-direction is 100 meters, and the object is launched from an angle of 25 degrees with an initial velocity of 5 m/s. I am asked to find the initial height at which the object is launched.

- Relevant Equations
- y=y0+vy0(t)-1/2gt^2,x=x0+vx0(t),v=v0+at, vy^2 = vy0^2-2g*change in y

First, I tried solving for the total time of flight, which I got as 100 = 5cos25*t --> t=22 s

Since we know the height at which the object lands, but not at which it is launched, I tried setting up the equation as:

yf = 40 - y0 = y0 + 5sin25*(22) - 1/2(9.8)(22)^2

However, I got y0 = 1183 m, which is not realistic given the problem statement. I assume this equation works if we only have freefall from an initial height.

I then tried solving for the the height at which vy = 0 (at max height):

0^2 = (5sin25)^2-2*9.8*deltay

delta y = 0.23 m

I also tried vy = v0y - gt for vy = 0 and got t = 0.22 s.

I don't know where to proceed from there. I also don't know if we need to change the sign of acceleration due to gravity when we consider motion past the point of maximum height.

Since we know the height at which the object lands, but not at which it is launched, I tried setting up the equation as:

yf = 40 - y0 = y0 + 5sin25*(22) - 1/2(9.8)(22)^2

However, I got y0 = 1183 m, which is not realistic given the problem statement. I assume this equation works if we only have freefall from an initial height.

I then tried solving for the the height at which vy = 0 (at max height):

0^2 = (5sin25)^2-2*9.8*deltay

delta y = 0.23 m

I also tried vy = v0y - gt for vy = 0 and got t = 0.22 s.

I don't know where to proceed from there. I also don't know if we need to change the sign of acceleration due to gravity when we consider motion past the point of maximum height.