From approximately what floor of a building


From approximately what floor of a building must a car be dropped from an at-rest position so that it reaches a speed of 80.7 ft/s (55 mi/h) when it hits the ground? Each floor is 12 ft higher than the one below it.

From approximately what floor of a building

Solution:

Show me the final answer↓

Let us use the following equation to find the solution to this problem:

v_2^2=v_1^2+2a_c(s_2-s_1)

(Where v_2 is final velocity, v_1 is initial velocity, a_c is constant acceleration, s_2 is initial displacement, and s_1 is final displacement)

 
From the question, we have the following given:

v_2=80.7 ft/s

v_1=0 ft/s

a_c=32.2 ft/s^2

s_1=0 ft

 

Substitute these values into our equation to find s_2.

v_2^2=v_1^2+2a_c(s_2-s_1)

80.7^2=0+2(32.3)(s_2-0)

s_2=101.1 ft

 

The question tells us that each floor is 12 ft apart, thus to figure out the floor number, we will divide the value of s_2 (height distance) by 12.

floor # = \dfrac{101.1}{12}=8.425

 
As we cannot have 0.425th of a floor, we will round to the upper integer which is the 9th floor.

 

Final Answer:

The car must fall from the 9th floor.

 

This question can be found in Engineering Mechanics: Dynamics, 13th edition, chapter 12, question 12-3.

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