Question

Tobias dropped a tennis ball from a height of 60 meters. The time in seconds it takes for the ball to fall 60 feet is 0.25(radical60). Find therr sets of approximations for the amount of time it will take. Then determine how long it will take for the ball to hit the ground.

Answer 1

We are given

Tobias dropped a tennis ball from a height of 60 meters. The time in seconds it takes for the ball to fall 60 feet is 0.25(radical60).

so, time is

$T=0.25\sqrt{60} =\frac{1}{4} \sqrt{60}$

we have to approximate it's value

First approximation set:

we know that

$49<60<64$

we can take sqrt all the sides

$\sqrt{49} <\sqrt{60} <\sqrt{64}$

we can simplify it

$7 <\sqrt{60} <8$

Divide all sides by 4

$\frac{7}{4}< \frac{1}{4} \sqrt{60} <\frac{8}{4}$

Second approximation set:

$7.7<\sqrt{60} <7.8$

Divide all sides by 4

$\frac{7.7}{4} <\frac{1}{4} \sqrt{60} <\frac{7.8}{4}$

$1.925<\frac{1}{4} \sqrt{60} <1.95$

Third approximation set:

$7.74<\sqrt{60} <7.75$

Divide all sides by 4

$\frac{7.74}{4} <\frac{1}{4} \sqrt{60} <\frac{7.75}{4}$

$1.935<\frac{1}{4} \sqrt{60} <1.9375$

so, we get

$t=1.94seconds$......Answer