Question

A penny is dropped from the top of the Empire State Building in New York City (h=381 m). Knowing that gravity accelerates the penny at a rate of –9.8 m/s 2 , with what velocity does the penny hit the ground? How long does it take to hit the ground?

Answer 1

Answer:

86.41 m/s : 8.8 sec

Explanation:

Here, 'coin is dropped' tells that the initial velocity of the coin is 0 & no force external force is applied except gravitational force.

Since, only gravitational force acts, gravity comes into play, in the direction of motion. Hence,

acceleration on coin = + g

u = initial velocity = 0

Let final velocity be 'v'.

Using equations of motion,

=> v² = u² + 2aS

=> v² = 0² + 2(g)(381)

=> v² = 2(9.8)(381)

=> v² = 7467.6

=> v = 86.4 m/s (approx)

Using v = u + at,

=> 86.4 = 0 + gt

=> 86.4/9.8 = t

=> 8.8 sec = t

Answer 2

GivEn :

Initial velocity of the ball (u) = 0 m/s

Distance from the top of a tower (s) = 20 m

Acceleration of the ball (a) = 10 m/s²

To find :

Final velocity or the speed required to hit the ground and the time taken = ?

SoluTion :

We'll solve this question by using the equations of motion.

Eqn used : v² = u² + 2as ; v = u + at

Substituting the values,

$\red{\begin{gathered}\implies \: \: \sf{v}^{2} - {u}^{2} = 2as \\ \\ \\\end{gathered} </p><p>}$

$\begin{gathered} \pink{\implies \: \: \sf{v}^{2} - {0}^{2} = 2 \times 10 \times 20 }\\ \\ \\\end{gathered} </p><p>$

$\begin{gathered}\implies \: \: \rm{v}^{2} = 400 \\ \\ \\\end{gathered}$

$\blue{\begin{gathered}\implies \: \: \sf v = 20 \: m {s}^{ - 1} \\ \\ \\\end{gathered} </p><p>}$

Now,

Time required by the ball to hit the ground :

$\begin{gathered}\implies \sf \: \: v = u + at \\ \\ \\\end{gathered} </p><p>$

$\begin{gathered}\implies \bf \: \: 20 = 0+ 10 \times t \\ \\ \\\end{gathered} </p><p>$

$\begin{gathered}\implies \sf \: \: 20 = 10t \\ \\ \\\end{gathered} </p><p>$

$\green{\begin{gathered}\implies \sf \: \: t = \cancel\dfrac{20}{10} \\ \\ \\\end{gathered} }$

$\begin{gathered}\implies \sf \: \: t = 2 \: s \\ \\ \\\end{gathered} </p><p>$

Therefore, the speed required to hit the ground is 20 m/s and the time taken to hit the ground is 2 s .