About how many meters is a 40-yard race

If a projectile is fired with an initial speed of vo ft/s at an angle α above the horizontal, then its position after t seconds

Elena L [17]

Answer:

a) The bullet hits the ground after 64 seconds.

b) The bullet hits the ground 113,511.7 feet away.

c) The maximum height attained by the bullet is of 16,384 feet.

Step-by-step explanation:

Equations of motion:

The equations of motion for the bullet are:

$x(t) = (v_0\cos{\alpha})t$

$y(t) = (v_0\sin{\alpha})t - 16t^2$

In which $v_0$ is the initial speed and $\alpha$ is the angle.

Initial speed of 2048 ft/s at an angle of 30o to the horizontal.

This means that $v_0 = 2048, \alpha = 30$ .

So

$x(t) = (v_0\cos{\alpha})t = (2048\cos{30})t = 1773.62t$

$y(t) = (v_0\sin{\alpha})t - 16t^2 = (2048\sin{30})t - 16t^2 = 1024t - 16t^2$

(a) After how many seconds will the bullet hit the ground?

It hits the ground when $y(t) = 0$ . So

$1024t - 16t^2 = 0$

$16t^2 - 1024t = 0$

$16t(t - 64) = 0$

16t = 0 -> t = 0 or t - 64 = 0 -> t = 64

The bullet hits the ground after 64 seconds.

(b) How far from the gun will the bullet hit the ground?

This is the horizontal distance, that is, the x value, x(64).

$x(64) = 1773.62(64) = 113511.7$

The bullet hits the ground 113,511.7 feet away.

(c) What is the maximum height attained by the bullet?

This is the value of y when it's derivative is 0.

We have that:

$y^{\prime}(t) = 1024 - 32t$

$1024 - 32t = 0$

$32t = 1024$

$t = \frac{1024}{32} = 32$

At this instant, the height is:

$y(32) = 1024(32) - 16(32)^2 = 16384$

The maximum height attained by the bullet is of 16,384 feet.

7 0

3 years ago

WILL GIVE BRAINLIEST if you show the steps

skelet666 [1.2K]

Answer:

i really dont know how to do this

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Use synthetic division to show that x is a solution of the third-degree polynomial equation, and use the result to factor the po

Flura [38]

You didn't state the value of x which you want to be shown to be a solution of the given polynomial

3x³ - 19x² + 30x - 8 = 0.

This polynomial of degree three obviously, has three solutions, and 2 is one of the solutions.

I will assume 2 to be the value of x you didn't state, and work with it. But the number is not 2, then it must be one of the remaining two solutions which would follow the same procedure that I will show here.

Answer:

The solutions to the equation

3x³ - 19x² + 30x - 8 = 0

are x = (2, 4, 1/3).

Step-by-step explanation:

Given the polynomial

3x³ - 19x² + 30x - 8 = 0

We need to show that x = 2 is a solution using synthetic division. If x = 2 is a solution, the remainder obtained from the synthetic division

(3x³ - 19x² + 30x - 8) ÷ (x - 2)

is zero.

SYNTHETIC DIVISION

2 | 3 ..... -19 ..... 30 ..... -8

................. 6 .... -26 ...... 8

.... 3........ -13 ........4 .......0->Remainder

Explanation:

The first row:

2 is from the divisor (x - 2). Always take the opposite of what you have. If the divisor is (x + 5), take -5.

(3, -19, 30, -8) are the coefficients of the divisor, the polynomial of degree three.

The coefficient of x³ is dropped to the third column.

2 is multiplied by 3 in the third column to obtain 6 in the second column.

6 is added to -19 to obtain -13.

Again, multiply 2 by -13 in the third column, to obtain -26 in the second column. Add this to 30 to obtain 4

Repeat this process, 2 × 4 = 8

8 + (-8) = 0.

Since 0 is the remainder, x = 2 is a solution to the polynomial.

The remaining factors can be found from the resulting polynomial of degree two whose coefficients were obtained from the synthetic division.

The coefficients of the polynomial are: 3, -13, 4

So, the polynomial is: 3x² - 13x + 4.

The zeros of this polynomial are the remaining factors we are looking for.

We solve

3x² - 13x + 4 = 0

(x - 4)(3x - 1) = 0

x - 4 = 0

=> x = 4

3x - 1 = 0

=> x = 1/3

x = 4, 1/3

The solutions to the equation are x = (2, 4, 1/3).

3 0

3 years ago

A triangle has side lengths of 10 cm, 24 cm, and 25 cm. Classify it as acute, obtuse, or right.

stepladder [879]

The FYI tells you that it is not a right triangle. The only way I know how to do this is with the Cos law. If you don't know what that is, you will have to draw it to scale.

The cos law tells me that it is acute (all three angles are under 90o). If you need me to show that to you, leave a note for me.

4 0

3 years ago

2. A ball is thrown into the air with an initial upward velocity of 48 ft/s. It height h in feet after t seconds is given by the

timurjin [86]

The first answer is the right one sjskememdlgsyendx

5 0

3 years ago