Mathematics, 30.07.2021 06:40, brittinyvenegas

The height of a projectile fired upward is given by the formula s = v0t − 16t2,
where s is the height in feet,
v0
is the initial velocity, and t is the time in seconds. Find the time for a projectile to reach a height of 96 ft if it has an initial velocity of 128 ft/s. Round to the nearest hundredth of a second.

Answers: 2

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answered: j015

The projectile will reach a height of 96 feet after about 0.84 seconds as well as after about 7.16 seconds.

Step-by-step explanation:

The height of a projectile fired upward is given by the formula:

$\displaystyle s = v_{0} t - 16t^2$

Where s is the height in feet, v₀ is the initial velocity, and t is the time in seconds.

Given a projectile with an initial velocity of 128 ft/s, we want to determine how long it will take the projectile to reach a height of 96 feet.

In other words, given that v₀ = 128, find t such that s = 96.

Substitute:

(96) = (128)t-16t^2

This is a quadratic. First, we can divide both sides by -16:

-6 = -8t+t^2

Isolate the equation:

t^2 - 8t + 6 = 0

The equation isn't factorable, so we can consider using the quadratic formula:

$\displaystyle t = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}$

In this case, a = 1, b = -8, and c = 6. Substitute:

$\displaystyle t = \frac{-(-8)\pm\sqrt{(-8)^2-4(1)(6)}}{2(1)}$

Simplify:

$\displaystyle t = \frac{8\pm\sqrt{40}}{2} = \frac{8\pm 2\sqrt{10}}{2} = 4\pm \sqrt{10}$

Hence, our two solutions are:

$\displaystyle t = 4+\sqrt{10} \approx 7.16\text{ or } t= 4-\sqrt{10} \approx 0.84$

So, the projectile will reach a height of 96 feet after about 0.84 seconds as well as after about 7.16 seconds.

answered: Guest

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

answered: Guest

f(x)=4

step-by-step explanation:

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The height of a projectile fired upward is given by the formula s = v0t − 16t2,
where s is th...