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 is0.25(√60).find three 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

time=t, hight =h t=√h over 4 or t=√h/4

Answer 1

Time taken to fall tennis ball from height of 60 m is 6.35330 seconds

The three sets of approximation of time is: t ≈ 6.353 seconds and t ≈ 6.35 seconds and t ≈ 6.4 seconds

Solution:

Given that 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 given by:

$0.25\sqrt{60} \text{ seconds }$  ---- eqn 1

Let us calculate time taken to fall tennis ball from height of 1 feet

time taken to fall tennis ball from height of 1 feet = time taken to fall tennis ball from height of 60 feet divided by 60

So Divide eqn 1 by 60

$\frac{0.25\sqrt{60}}{60} \text{ seconds }$

Since Tobias dropped a tennis ball from a height of 60 meters, let us convert 60 meters to foot

1 meter = 3.28084 foot

60 meter = 196.85 foot

Therefore, Time taken to fall tennis ball from height of 60 m is given as:

$\rightarrow \frac{0.25\sqrt{60}}{60} \times 196.85 \\\\\rightarrow \frac{1.9364}{60} \times 196.85\\\\\rightarrow 0.03227 \times 196.85\\\\\rightarrow 6.35330$

Thus Time taken to fall tennis ball from height of 60 m is 6.35330 seconds

Finding three sets of approximations for the amount of time:

t = 6.35330 seconds

We can round to first three decimal places and then two decimal places and then one decimal place

First look at the digit to immediate right of rounding off digit

If that digit is less than 5, do not change the rounding digit but drop all digits to the right of it.

If that digit is greater than or equal to five, add one to the rounding digit and drop all digits to the right of it.

To the nearest thousandth:

t ≈ 6.353 seconds

To the nearest hundredth

t ≈ 6.35 seconds

To the nearest tenth

t ≈ 6.4 seconds