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?

Answers: 3

Show answers

Answers

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;

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

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

Learn more here: link

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

Do the inverse operation

Answer from: Quest

answer: x=60

Can someone plz answer this for me? whoever answers it first, i will give !

Another question on Mathematics

Mathematics, 21.06.2019 13:30

Estimate the product. round the first factor to the nearest whole number, round the second factor to the nearest ten, and then multiply. 3 8/9 × 96

Answers: 3

Answer

Mathematics, 21.06.2019 19:30

Last month, a 770 g box of cereal was sold at a grocery store for $3.10. however, this month, the cereal manufacturer launched the same cereal in a 640 g box, which is being sold at $2.50. what is the percent change in the unit price?

Answers: 1

Answer

Mathematics, 21.06.2019 21:50

Match each whole number with a rational, exponential expression 3 square root 27^2find the domain and range of the exponential function h(x)=125^x. explain your findings. as x decreases does h increase or decrease? explain. as x increases does h increase or decrease? explain.

Answers: 3

Answer

Mathematics, 21.06.2019 23:00

Someone answer this asap for the first five terms of a sequence are shown. 5, 11, 23, 47, 95, . . which recursive function defines the nth term in the sequence for n > 1? a. f(n) = f(n - 1) + 6 b) f(n) = f(n - 1) + 48 c) f(n) = 3 • f(n - 1) + 1 d) f(n) = 3 • f(n - 1) - 4

Answers: 1

Answer

You know the right answer?

The height (in meters) of a projectile shot vertically upward from a point 4 m above ground level wi...

Questions