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 melons to fly off the truck. One melon rolls over the edge with an initial speed vi = 13.3 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 edge of the road, and with the equation y2 = (20.0 m)x, where x and y are measured in meters. What are the x- and y-coordinates of the melon when it splatters on the bank?

Explanation / Answer

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 = 13.3 t and for the y value y=1/2 gt^2 now, we can make this an expression in x recalling that for this projectile, x=13.3t, so that t=x/13.3; substitute this into the y equation and get y=1/2 gt^2 = 1/2 g(x/13.3)^2 = 0.028 x^2 now, we want to know when this curve intersects y^2=20x y=Sqrt[20x]=0.028x^2 square both sides 20x= 0.000784 x^4 25510.2=x^3 => x=29.43m when x=29.43, y=Sqrt(20*29.43)=24.26m, so the impact occurs 24.26m down, 29.43 m beyond the ledge

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.