Question

Dejamos caer un objeto desde lo alto de una torre y medimos el tiempo que tarda en llegar al suelo que resulta ser de 0,02 minutos. calcula :a) la altura de la torre, b) la velocidad al impactar al suelo.

Answer 1

Answer: a) 11.76 m/s  b) 7.056 m

Explanation:

The described situation is as follows:

An object is dropped from the top of a tower and when measuring the time it takes to reach the ground that turns out to be 0.02 minutes.

This situation is related to free fall, this also means we have constant acceleration, hence the equations we will use are:

$V_{f}=V_{o}+at$ (1)  

${V_{f}}^{2}={V_{o}}^{2}+2ad$ (2)  

Where:  

$V_{f}$ Is the final velocity of the object

$V_{o}=0$ Is the initial velocity of the object (it was dropped)

$a=9.8 m/s^{2}$ is the acceleration due gravity

$d$ is the height of the tower

$t=0.02min=1.2 s$ is the time it takes to the object to reach the ground

b) Begining with (1):

$V_{f}=0+at$ (3)  

$V_{f}=at=(9.8 m/s^{2})(1.2 s)$ (4)  

$V_{f}=11.76 m/s$ (5)  This is the final velocity of the object

a) Substituting (5) in (2):

$(11.76 m/s)^{2}=0+2(9.8 m/s^{2})d$ (6)  

Clearing $d$:

$d=\frac{(11.76 m/s)^{2}}{2(9.8 m/s^{2})}$ (7)  

$d=7.056 m$ (8)  This is the height of the tower