A catapult is used to launch large projectiles long distances. Suppose that the

Question

A catapult is used to launch large projectiles long distances. Suppose that the height of a piano off the ground h, in feet, is a function of the horizontal distance along the ground in the direction it is thrown, x, also in feet. Given h-f(x)- -0.002x 0.6x+ 60, answer the following questions a) Find the vertex. Explain what the vertex means in context of the problem The vertex isThis represents the maximum height of feet that occursfeet horizontally from the launch point. b) If you want to crush a Volkswagen bug with the piano, how far from the catapult should the car be? It should be approximately feet in front of the catapult. (Round answer to nearest tenth.)

Explanation / Answer

f(x) = -0.002x^2 + 0.6x + 60

a) writing the equation in vertex form

-.002 ( x^2 - 300 x ) + 60

-.002 ( x - 150 )^2 + 45 + 60

= -.002 ( x - 150 )^2 + 105

vertex is ( 150 , 105 )

this represents the maximum height of 105 feet that occurs 150 feet horzontally

b) setting the equation to 0

-0.002x^2 + 0.6x + 60 = 0

solving for x

x = 379.13

it should be approximately 379.13 feet infront of catapult

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