Answer to Question #293107 in Analytic Geometry for kyumi

Question

A truck hauling a cylindrical steel ta

nk has to pass under an overhead parabolic arch bridge

which has span of 7.32m and 6.10m high. If the tank is 1.83m in

diameteris placed in the truck with sides vertical, and the top of the tank is 3.05m above the street level, can the truck pass the bridge? If so,what is the smallest clearance from the top of the tank

Answer 1

Define the ground to where the truck tires are driving on.

if the highest point on the bridge is 6.10m off the ground, then this means that the top of the cylinder must be lower than 6.10m off the ground.

However, the truck bed is 3.05m off the ground and the cylinder diameter is 1.83m, so we have a total of ( 3.05 + 1.83)m = 4.88m

The top of the cylinder 4.88m is lower off the ground compared to the vertex of the bridge ( 6.10m)

Therefore, we may conclude that the truck can pass under the bridge.

Thus the smallest clearance from the top of the tank is 4.88m