Please Solve it Following the legendary battle at the fortress of Hornburg, the

Question

Please Solve it

Following the legendary battle at the fortress of Hornburg, the wizard Gandalf managed to lay his hands on some of the "blasting-fire" that was used to destroy a section of the fortress wall during the battle. Gandalf, a man of magic and science quickly discovered that igniting this "blasting-fire" in a cylinder that was sealed at one end and open at the other created a directed explosion. Further-more. if some object were placed between the opening to the cylinder and the "blasting-fire", said object would be thrown from the cylinder at a great force in the direction the opening was pointed. Naturally Gandalf thought of many different types of objects to be thrown but he settled on a fully armored Hobbit. To Gandalf, all else paled in comparison to the havoc that such a thing could bring on the enemy forces. The tactical advantages were endless! However, Gandalf was concerned for the safety of Hobbits and wanted some numbers crunched before he launched a Hobbit. So, after firing several sandbags (of approximate weight and size) from his cannon, which he dubbed the "Halfling Hurler +2", he came up with the following formula to model the approximate height (in feet) of the flying Hobbit over a given time t in seconds: h(t) = (55 )t - 16t2 + 3 Approaching his friend, Odo Proudfoot, Gandalf asked for an approximation 011 the vertical velocity of the hobbit when it hits the ground. What is the vertical velocity of the hobbit when it hits the ground?

Explanation / Answer

h(t) is actually a parabola. (You can verify it yourself when you do a smart rearrangement of the terms)

Anyway, when the Hobbit hits the ground,

h(t) = 0

55sqrt(2)* t - 16* t^2 + 3 = 0

solving for t, we get

t = 4.9 sec

(OR)

t = -0.04 s

Hence t = 4.9 sec

vertical velocity is given by

dh/dt = 55sqrt(2) - 32* t

At t = 4.9 sec,

The vertical velocity of the hobbit would be = 55sqrt(2) - 32 * 4.9

= -79 feet /sec

The negative sign dennotes the downward velocity!

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