Posted by Anonymous on Monday, June 10, 2013 at 5:32pm.
Berry is standing at the edge of a hill that slopes downward and to the right. He notices that for every 5 feet you go in a horizontal direction, the hill drops by 2 feet. Berry places a ball at the edge of the hill (the origin of the coordinate system), and kicks the ball at a speed of 20 m/s and at an angle of 30o to the horizontal. The equation describing the ballâ€™s height as a function of the horizontal distance it travels is given by . How far down the hill does the ball land?

precalculus  Steve, Monday, June 10, 2013 at 6:00pm
the velocity has horizontal and vertical components
Vx = 20(√3/2) = 17.32
Vy = 20(1/2) = 10.00
The horizontal and vertical positions of the ball are thus
sx = 17.32t
sy = 10.00t  4.9t^2
So, the xy function of the height is
y = 10.00(x/17.32)  4.9(x/17.32)^2
= 0.01633x^2 + 0.5774x
The ground is descending with slope = 2/5 so the surface is given by
y = 2/5 x
So, where does the parabola intersect the line?
0.01633x^2 + 0.5774x = 0.4x
x = 59.85
y = 23.94
so the distance down the slope is
d = √(59.85^2 + 23.94^2) = 64.46 m
Answer This Question
Related Questions
 precalculus  Berry is standing at the edge of a hill that slopes downward and ...
 Math help please  Which hill described in the table is the steepest? Explain. ...
 Math  9.)Which hill described in the table is the steepest? Explain.' (Table) ...
 math  Street  Horizontal  Vertical rise Distance ft. of street ft. _______...
 Math "Need Help Asap"!  9.)Which hill described in the table is the steepest? ...
 math  Which hill described in the table is the steepest? (Table) Street: ...
 Math  Which hill described in the table is the steepest? (Table) Street: ...
 Math  9.)Which hill described in the table is the steepest? Explain.' (Table) ...
 math help please  Which hill described in the table is the steepest and why? ...
 Pre Algebra  Which hill described in the table is the steepest and why? Street...
More Related Questions