A truck loaded with cannonball watermelons stops suddenly to avoid running over

Question

A truck loaded with cannonball watermelons stops suddenly to avoid running over the edge of a washed out bridge see figure. The quick stop causes a number of mentions to fly off the truck. One melon rolls over the edge with an initial speed v_2 = 16.0 m/s in the horizontal direction. A cross section of the bank has the shape of the bottom half of a parabola, with its vertex at the initial location of the projected watermelon and with the equation y^2 = 8x, when x and y are measured in meters. What are the x and y coordinates of the melon when it splatters on the bank? Your response differs from the correct answer by more than 10%. Double check your calculations. Your response differs from the correct answer by more than 100%

Explanation / Answer

we need to write the equation of motion of the projectile;

let's call down the positive y direction to make life simple and consistent,

for the component of the projectile, we have that x = 16* t

and for the y value y=1/2* g*t^2

now, we can make this an expression in x recalling that for this projectile, x=16*t, so that

t = x/16; substitute this into the y equation and get

y=1/2 gt^2 = 1/2 g(x/16)^2 = 0.019* x^2

now, we want to know when this curve intersects y^2=8*x

y=Sqrt[8x] = 0.019*x^2

square both sides

8 x = 0.000363* x^4

22038.56 = x^3
x = 27.11

when x=27.11,

y = Sqrt[8*27.11] = 14.72 m, so the impact occurs 17.72 m down, 27.11 m beyond the ledge

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