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Wed 27 Oct, 2004 06:12 pm
Help me with this question.....
You can kick a soccer ball 28m on level ground, giving it an initial velocity at 40 degrees to the horizontal. At the same initial velocity and angle to the horizontal, what horizontal distance can you kick the ball on a 15 degree upward slope.
1) make 2 equations using the x,a,t equation for vertical and horizontal motion. these 2 equations will each have time and initial velocity unknown (use SOH CAH TOA)...so using these 2 equations, you can solve for the 2 unknowns and figure out initial velocity magnitude and time in the air
2) now that you know initial velocity, figure out the time in the air if you were to launch it at the new angle by calculating the effective upward velocity at the new angle
3) now that you know the time in the air for the new angle, you can find the distance travelled if you assume there is no drag force
Based on the statement of the problem ("same initial velocity and angle to the horizontal," "kick the ball on a 15 degree upward slope"), it seems to me that the solution is the X-coordinate of the intersection of the parabola that describes the flight of the ball (kicked at (0,0)) and the line with slope tan(15) that passes through (0,0).
I get 28*(1-tan(15)/tan(40)).