Question

The top floor of the Ostankino TV Tower in Moscow is located at a height of 360.4 m. Assume a stone is dropped from this top floor. [Note: round your numerical answers to two decimal places; if necessary]

(a) Find the distance of the stone above the ground at any time t (before it hits the ground)

(b) How long does it take the stone to reach the ground?

(c) With what velocity does it reach the ground?

Answer 1

Answer:

$x=360.4-4.905t^2$

8.57181 s

84.0894561 m/s

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

g = Acceleration due to gravity = 9.81 m/s² = a

Let distance from ground be x

From equation of motion we have

$s=ut+\frac{1}{2}at^2$

Here, distance covered while the stone is falling will be $360.4-x$

$360.4-x=ut+\frac{1}{2}at^2\\\Rightarrow 360.4-x=\frac{1}{2}9.81t^2\\\Rightarrow 360.4-x=4.905t^2\\\Rightarrow x=360.4-4.905t^2$

The equation is $x=360.4-4.905t^2$

At the ground x = 0

$0=360.4-4.905t^2\\\Rightarrow t=\sqrt{\dfrac{-360.4}{-4.905}}\\\Rightarrow t=8.57181\ s$

The time taken by the stone to fall to the ground is 8.57181 s

$v=u+at\\\Rightarrow v=0+9.81\times 8.57181\\\Rightarrow v=84.0894561\ m/s$

The velocity of the stone when it reaches the ground is 84.0894561 m/s