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3 years ago

10

Terrence and his family are enjoying a vacation in the wild west. One place they really want to visit is the Grand Canyon. The t

otal distance they will drive is 400 miles. If they have already driven 280 miles, what percent have they driven?

1 answer:

bonufazy [111]3 years ago

6 0

Answer: 70 percent

Step-by-step explanation:

280 divided by 400 is 0.70, so 280 is 70 percent of 400.

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A ball is launched upward at 14 m/s from a platform 30 m high.Find the maximum height the ball will reach and how long it will t

BartSMP [9]

Answer:

The ball will reach a maximum height of 39.993 meters after 1.428 seconds.

Step-by-step explanation:

Let suppose that no non-conservative forces acts on the ball during its motion, then we can determine the maximum height reached by the Principle of Energy Conservation, which states that:

$K_{1}+U_{g,1} = K_{2}+U_{g,2}$ (1)

Where:

$K_{1}$ , $K_{2}$ - Initial and final translational kinetic energies, measured in joules.

$U_{g,1}$ , $U_{g,2}$ - Initial and final gravitational potential energies, measured in joules.

By definition of translational kinetic energy and gravitational potential energy we expand and simplify the expression above:

$\frac{1}{2}\cdot m\cdot v_{2}^{2}+m\cdot g\cdot y_{2}= \frac{1}{2}\cdot m\cdot v_{1}^{2}+m\cdot g\cdot y_{1}$ (2)

Where:

$m$ - Mass of the ball, measured in kilograms.

$g$ - Gravitational acceleration, measured in meters per square second.

$v_{1}$ , $v_{2}$ - Initial and final speed of the ball, measured in meters per second.

$y_{1}$ , $y_{2}$ - Initial and final heights of the ball, measured in meters.

The final height of the ball is determined by the following formula:

$v_{2}^{2}+2\cdot g\cdot y_{2} = v_{1}^{2}+2\cdot g\cdot y_{1}$

$v_{1}^{2}-v_{2}^{2}+2\cdot g \cdot y_{1}=2\cdot g\cdot y_{2}$

$y_{2} = y_{1}+\frac{v_{1}^{2}-v_{2}^{2}}{2\cdot g}$ (3)

If we know that $y_{1} = 30\,m$ , $v_{1} = 14\,\frac{m}{s}$ , $v_{2} = 0\,\frac{m}{s}$ and $g = 9.807\,\frac{m}{s^{2}}$ , the maximum height that the ball will reach is:

$y_{2} = 30\,m + \frac{\left(14\,\frac{m}{s} \right)^{2}-\left(0\,\frac{m}{s} \right)^{2}}{2\cdot \left(9.807\,\frac{m}{s^{2}} \right)}$

$y_{2} = 39.993\,m$

The ball will reach a maximum height of 39.993 meters.

Given the absence of non-conservative forces, the ball exhibits a free fall. The time needed for the ball to reach its maximum height is computed from the following kinematic formula:

$t = \frac{v_{2}-v_{1}}{-g}$ (4)

If we know that $v_{1} = 14\,\frac{m}{s}$ , $v_{2} = 0\,\frac{m}{s}$ and $g = 9.807\,\frac{m}{s^{2}}$ , then:

$t = \frac{0\,\frac{m}{s}-14\,\frac{m}{s} }{-9.807\,\frac{m}{s^{2}} }$

$t = 1.428\,s$

The ball will take 1.428 seconds to reach its maximum height.

6 0

3 years ago

The length of a rectangle is 4

Juli2301 [7.4K]

Answer:

w=16, L=20

Step-by-step explanation:Length(L)=w+4

P=72

P=2L+2w

P=2(w+4)+ 2w

P=2w+8+2w

72=4w+8

4w=72-8

4w=64(/4)

w=16

L=16+4=20

Verification: 16+16+20+20=72

32+40=72

72=72 (T)

4 0

3 years ago

At 5 seconds, an object's velocity is 9 meters per second. At 8 seconds, the object's velocity is 25 meters per second. Assuming

ivanzaharov [21]

The formula for acceleration is (∆v)/(∆t), or (final velocity - initial velocity)/(final time - initial time). If you input your values the problem would work out as followed:

A = <span>(∆v)/(∆t)
A = (25-9)/(8-5)
A = 16/3
A = 21.33 (rounded to the nearest hundredth)</span>

8 0

3 years ago

tatuchka [14]

Answer:

8 inches

Step-by-step explanation:

4 feet is 48 inches. So 48/6=8

Hope that helps

3 0

3 years ago

Read 2 more answers

How can I calculate the area for polygons

erica [24]

Answer:

Step-by-step explanation:

Area is one-half times the perimeter times the apothem

4 0

3 years ago