Question

An object dropped from a height of 600 feet has a height, h(t), in feet after t seconds have elapsed, such that h(t) = 600 − 16t 2 . Express t as a function of height h, and find the time to reach a height of 400 feet.

Answer 1

given h = 600 - 16t ( add 16t to both sides )

16t + h = 600 ( subtract h from both sides )

16t = 600 - h ( divide both sides by 16 )

t = $\frac{600-h}{16}$

when h = 400

t = $\frac{600-400}{16}$ = $\frac{200}{16}$ = 12.5 seconds

Answer 2

Answer:

The required time is 3.54 seconds approximately or $\frac{5}{2}\sqrt{2}$ seconds.

Step-by-step explanation:

Consider the provided function.

$h(t) = 600-16t^2$

Where t represents the time in seconds and h represents the height.

It is given that we need to find the time to reach a height of 400 feet.

Substitute h(t)=400 in the above function.

$400= 600-16t^2$

$400- 600=-16t^2$

$-200=-16t^2$

$200=16t^2$

$\frac{50}{4}=t^2$

$t=\sqrt{\frac{50}{4}} \\t=\frac{5}{2}\sqrt{2}$

Neglect the negative value as time should be a positive number.

Or

$t\approx 3.54$

Hence, the required time is 3.54 seconds approximately.