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3 years ago

11

A rocket starting from its launch pad is subjected to a uniform acceleration of 100 meters/second2. Determine the time needed to

reach the final velocity of 1,000 meters/second.

1 answer:

balandron [24]3 years ago

5 0

The velocity is the integral of acceleration. If acceleration is 100 m/s^2 then velocity is:

$v= \int\limits^{}_{}100 \, dt=100t$

So to know the velocity at any time, t, we just put t in seconds into this equation. To know at what time we get to a certain velocity, we set this equation equal to that velocity and solve for t:

$100t = 1000 \\ \\ t= \frac{1000}{100} =10s$

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A farmer lifts his hay bales into the top loft of his barn by walking his horse forward with a constant velocity of 1 ft/s. Dete

Lesechka [4]

Answer:

The velocity of the hay bale is - 0.5 ft/s and the acceleration is $6.25\times 10^{- 3} ft/s^{2}$

Solution:

As per the question:

Constant velocity of the horse in the horizontal, $v_{x} = 1 ft/s$

Distance of the horse on the horizontal axis, x = 10 ft

Vertical distance, y = 20 ft

Now,

Apply Pythagoras theorem to find the length:

$20^{2} + 10^{2} = l^{2}$

$l^{2}= 500$

Now,

$x^{2} + y^{2} = 500$ (1)

Differentiating equation (1) w.r.t 't':

$2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0$

$x\frac{dx}{dt} = - y\frac{dy}{dt}$

where

$\frac{dx}{dt}$ = Rate of change of displacement along the horizontal

$\frac{dy}{dt}$ = Rate of change of displacement along the vertical

$v_{x}$ = velocity along the x-axis.

$v_{y}$ = velocity along the y-axis

$xv_{x} = -yv_{y}$

$v_{y} = - 10\times \frac{1}{20} = - 0.5 ft/s$

$|v_{y}| = 0.5\ ft/s$

Acceleration of the hay bale is given by the kinematic equation:

$v_{y}^{2} = u_{y} + 2ay$

$(-0.5)^{2} =0 + 2ay$

$0.25 = 2ay$

$\frac{0.25}{2y} = a$

$a = \frac{0.25}{2\times 20} = 6.25\times 10^{- 3} ft/s^{2}$

7 0

3 years ago

Find the distance traveled by a particle with position (x, y) as t varies in the given time interval. x = 2 sin2(t), y = 2 cos2(

Tanya [424]

The distance traveled by the particle at the given time interval is 0.28 m.

<h3>Position of the particle at time, t = 0</h3>

The position of the particle at the given time is calculated as follows;

x = 2 sin2(t)

y = 2 cos2(t)

x(0) = 2 sin2(0) = 0

y(0) = 2 cos2(0) = 2(1) = 2

<h3>Position of the particle at time, t = 4</h3>

x = 2 sin2(t)

y = 2 cos2(t)

x(4) = 2 sin2(4) = 0.28

y(4) = 2 cos2(4) = 2(1) = 1.98

<h3>Distance traveled by the particle at the given time interval</h3>

d = √[(x₄ - x₀)² + (y₄ - y₀)²]

d = √[(0.28 - 0)² + (1.98 - 2)²]

d = 0.28 m

Thus, the distance traveled by the particle at the given time interval is 0.28 m.

Learn more about distance here: brainly.com/question/23848540

#SPJ1

7 0

1 year ago

a car accelerates from 4 meters/second to 16 meter/second in 4 seconds. The cars acceleration is how many meter/seconds.

Allushta [10]

Answer:

=3 metre per second ^2

Explanation:

Formula for acceleration is

V-U÷T

In the given information

V=16

U=4

T=4

Acceleration =16-4/4

=3 metre per second ^2

4 0

3 years ago

According to the three laws of planetary motion, planetary orbits are in the shape of a/an

Talja [164]

<span>According to the three laws of planetary motion, planetary orbits are in the shape of an "Ellipse"

In short, Your Answer would be Option B

Hope this helps!</span>

8 0

3 years ago

What is the scientific definition of tracked?

dexar [7]

To find or discover by investigation?

8 0

3 years ago