Mathematics, 26.03.2020 00:31 jose0765678755

The height (in meters) of a projectile shot vertically upward from a point 4 m above ground level with an initial velocity of 25.5 m/s is h = 4 + 25.5t − 4.9t2 after t seconds. (Round your answers to two decimal places.)(a) Find the velocity after 2 s and after 4 s. v(2) = 5.9 Correct: Your answer is correct. m/s v(4) = -13.7 Correct: Your answer is correct. m/s (b) When does the projectile reach its maximum height? (c) What is the maximum height? (d) When does it hit the ground? (e) With what velocity does it hit the ground?

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Answer from: hcortez4023

(a) The velocity of the projectile after 2 s and 4 s is 5.9 m/s and -13.7 m/s respectively.

(b) the projectile will reach maximum height in 2.6 s.

(d) The time for the projectile to fall to the ground is 2.76 s

(e) The velocity with which the projectile hits the ground is 27.1 m/s.

The given equation;

h = 4 + 25.5t - 4.9t^2

(a) the velocity after 2 s and 4 s

$v = \frac{dh}{dt} = 25.5 - 9.8t\\\\v(2) = 25.5 - 9.8(2)\\\\v(2) = 5.9 \ m/s\\\\v(4) = 25.5 - 9.8(4)\\\\v(4) = -13.7 \ m/s$

(b) when the projectile reaches maximum height the final velocity is zero.

$v = \frac{dh}{dt} = 0\\\\\frac{dh}{dt} = 25.5 - 9.8t = 0\\\\9.8t = 25.5\\\\t= \frac{25.5}{9.8} = 2.6 \ s$

Thus, the projectile will reach maximum height in 2.6 s.

$h = 4 + 25.5t - 4.9t^2\\\\h(2.6) = 4 + 25.5(2.6) - 4.9(2.6^2)\\\\h(2.6) = 37.18 \ m$

(d) The time for the projectile to fall to the ground is calculated as;

$h = v_y_0 t + \frac{1}{2} gt^2\\\\37.18 = 0 + 0.5\times 9.8t^2\\\\37.18 = 4.9t^2\\\\t^2 = \frac{37.18}{4.9} \\\\t^2 = 7.588\\\\t = \sqrt{7.588} \\\\t = 2.76 \ s$

(e) when the projectile hits the ground, the velocity will be maximum;

$v'' =\frac{d^2h}{dt^2} = -9.8$

$v_f= v_0 + gt\\\\v_f = 0 + 9.8\times 2.76\\\\v_f = 27.1 \ m/s$

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Answer from: crystalrc3414

(a) The velocity after 2 second is 5.9 m/s

The velocity after 4 second is -13.7 m/s.

(b) The projectile reaches its maximum height after 2.60 s of projection.

(c)The maximum height that is attained by the projectile is 37.18 m.

(d)Therefore the projectile hits the ground after 5.36 seconds of projection.

(e)The velocity of the projectile when it hits the ground is 27.03 m/s

Step-by-step explanation:

Given that, a projectile shot vertically upward from a point 4 m above the ground with a initial velocity of 25.5 m/s.

The height of the projectile after t seconds is

h=4+25.5t-4.9t^2

where h is in meter.

(a)

We use the formula

v=u+at

V= final velocity

u = initial velocity = 25.5 m/s

a = acceleration= acceleration due to gravity= 9.8 m/s²

Since the object moves upward direction and acceleration due to gravity is downward direction. So here a= -9.8 m/s.

v(2)= 25.5+(-9.8)×2

=25.5-19.6

=5.9 m/s

And when t= 4

v(4)= 25.5+(-9.8)×4

=25.5-39.2

= -13.7 m/s

The velocity after 2 second is 5.9 m/s

The velocity after 4 second is -13.7 m/s.

(b)

At its maximum height,the velocity of the projectile is zero. i.e v=0

∴0=25.5+(-9.8)t

⇒9.8t=25.5

$\Rightarrow t=\frac{25.5}{9.8}$

⇒t = 2.60 s

The projectile reaches its maximum height 2.60 s after projection.

(c)

To find the maximum height, we are putting t= 2.60 in this equation h=4+25.5t-4.9t^2 .

$\therefore h= 4+(25.5\times 2.60)-(4.9\times 2.60^2)$

=37.18 m

The maximum height that is attained by the projectile is 37.18 m.

(d)

When the projectile hits the ground the height will be zero i.e h=0

From the equation of height we get

$\therefore h=0=4+25.5t-4.9t^2$

$\Rightarrow 4+25.5t-4.9t^2=0$

$\Rightarrow t=\frac{-25.5\pm\sqrt{25.5^2-4(-4.9).4}}{2(-4.9)}$

⇒t= -0.15 ,5.36

Therefore it hits the ground after 5.36 seconds of projection.

(e)

To find the velocity we use the formula v=u+at

Here v = final velocity=?

u=25.5 m/s,

t = 5.36 s

a= -9.8m/s²

v=25.5+(-9.8)5.36

= -27.03 m/s

Negative sign denoted that the motion of the projectile is downward direction.

The velocity of the projectile when it hits the ground is 27.03 m/s.

Answer from: Quest

B. 16is the absolute value

Answer from: Quest

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

$a=9\times 12=108\text {ft^2}$

so the area of the floor is 108 square feet, converting that into square yards we get,

$108 \times 0.1111= 12 \text{yd^2}$

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

$\$15 \times 12=\$180$

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

$a = 12 \times 15=180\text {ft}^2$

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

$180 \times 0.111=20 \text {yd}^2$

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

$\$15 \times 20= \$300$

so, it will cost $300.

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