The amount of time it takes an object dropped from an initial height of h0 feet to reach a height of h feet is given by the formula $t = \sqrt { \frac { h _ { 0 } - h } { 16 } }$ If it takes an object dropped from the top of the Empire State Building in New York 6.6 seconds to land on top Of an adjacent building that is 550 feet tall, approximate the height of the Empire State Building to the Nearest foot.
A) 1,150 feet
B) 1,247 feet
C) 1,120 feet
D) 1,020 feet

Question

Quizplus · Accepted Answer

Given $t = 6.6$ seconds and the height of the adjacent building $h = 550$ feet, we can use the formula $t = \sqrt { \frac { h _ { 0 } - h } { 16 } }$ to find $h_0$, the height of the Empire State Building. Plugging in the values, we get $6.6 = \sqrt { \frac { h _ { 0 } - 550 } { 16 } }$. Squaring both sides gives $43.56 = \frac { h _ { 0 } - 550 } { 16 }$, and solving for $h_0$ gives $h_0 = 43.56 \times 16 + 550 = 1247$. Therefore, the approximate height of the Empire State Building is 1,247 feet.

The Amount of Time It Takes an Object Dropped from an Initial