What are the intercepts of the graphed function?

A baseball is hit almost straight up into the air with a speed of 26 m/s . Estimate how high it goes.

Natalka [10]

Answer:

The maximum height of the ball is 34.5 m.

The ball is 5.31 s in the air.

Explanation:

Hi there!

The equations for the height and velocity of the baseball that is hit straight up are as follows:

y = y0 + v0 · t + 1/2 · g · t²

v = v0 + g · t

Where:

y = height of the baseball at time t.

y0 = initial height.

v0 = initial velocity.

t = time.

g = acceleration due to gravity (-9.8 m/s² considering the upward direction as positive).

v = velocity at time t.

If we place the origin of the frame of reference at the place where the baseball is hit, then, y0 = 0.

To calculate how high it goes, we have to obtain the time at which the ball is at maximum height. At that point, the velocity is 0. Then using the equation of velocity:

v = v0 + g · t

0 = 26 m/s - 9.8 m/s² · t

-26 m/s / -9.8 m/s² = t

t = 2.65 s

The height at that time will be the maximum height:

y = y0 + v0 · t + 1/2 · g · t² (y0 = 0)

y = 26 m/s · 2.65 s - 1/2 · 9.8 m/s² · (2.65 s)²

y = 34.5 m

The maximum height of the ball is 34.5 m

If it takes the ball 2.65 s to reach the maximum height it will take another 2.65 s to return to the initial position. Then, the time it will be in the air is (2.65 s + 2.65 s) 5.30 s. However, let´s calculate the time it takes the ball to reach the initial position using the equation for height.

At the initial position y = 0. Then:

y = y0 + v0 · t + 1/2 · g · t² (y0 = 0)

0 = 26 m/s · t - 1/2 · 9.8 m/s² · t²

0 = t (26 m/s - 1/2 · 9.8 m/s² · t) (t = 0 when the ball is hit)

0 = 26 m/s - 1/2 · 9.8 m/s² · t

-26 / -4.9 m/s² = t

t = 5.31 s ( the difference with the 5.30 s obtained above is due to rounding the time to 2.65 s).

The ball is 5.31 s in the air.

Have a nice day!

5 0

3 years ago

The plates of a parallel-plate capacitor are 2.50 mm apart, and each carries a charge of magnitude 80.0 nC. The plates are in va

bonufazy [111]

Answer:

10000 V

0.00225988700565 m²

$8\times 10^{-12}\ F$

Explanation:

E = Electric field = $4\times 10^6\ V/m$

d = Gap = 2.5 mm

Q = Charge = 80 nC

$\epsilon_0$ = Permittivity of free space = $8.85\times 10^{-12}\ F/m$

Potential difference is given by

$V=Ed\\\Rightarrow V=4\times 10^6\times 2.5\times 10^{-3}\\\Rightarrow V=10000\ V$

The potential difference between the plates is 10000 V

Area is given by

$A=\dfrac{Q}{\epsilon_0E}\\\Rightarrow A=\dfrac{80\times 10^{-9}}{8.85\times 10^{-12}\times 4\times 10^6}\\\Rightarrow A=0.00225988700565\ m^2$

The area of the plate is 0.00225988700565 m²

Capacitance is given by

$C=\dfrac{\epsilon_0A}{d}\\\Rightarrow C=\dfrac{8.85\times 10^{-12}\times 0.00225988700565}{2.5\times 10^{-3}}\\\Rightarrow C=8\times 10^{-12}\ F$

The capacitance is $8\times 10^{-12}\ F$

4 0

3 years ago

You have two windlasses (winches) named X and Y. Windlass X drum diameter is 50cm and windlass Y drum diameter is 75cm. Both are

Blababa [14]

You have two windlasses named X and Y. Windlass X drum diameter is 50cm and windlass Y drum diameter is 75cm. Both are hoisting a 50kg weight, Hence, X will lift faster and easier than Y

<h3>What is windlasses (winches) will lift faster?</h3>

Generally, the equation for the Torque is mathematically given as

Torque(X)=weight x radius of drum

T=50x9.81x0.25

T=122.625 Nm

For, Torque (Y)

T=50x9.81x0.375

T=183.93 Nm

Generally, the equation for the Equation of Power is mathematically given as

P= Torque * Angular velocity

Angular velocity (w)= 2 x pi x N/60

As a consequence, torque has an inverse relationship to speed. Because of this, the torque will decrease as the speed rises.

According to the previous statement, windlass X has a speed of lift that is at its maximum, but windlass Y has a speed that is very low.

Additionally, power is exactly proportional to torque, which means that the highest possible torque required the highest possible amount of energy and vice versa.

Therefore, X should raise at the highest possible speed while using the least amount of energy.

In conclusion, X will lift faster and easier than Y

Read more about windlasses

brainly.com/question/14289204

#SPJ1

4 0

2 years ago

Which of the following is quantitative data? a. Color c. Shape b. Odor d. Volume

Papessa [141]

Hello there! Quantitive data has to do with measurements that can be shown with numbers. Examples of this are things like your height and the length of your arms. With that alone, A and B are eliminated, because those answer choices make no sense. They can't be expressed by numbers and you can't measure colors or odors mathematically. Volume is a way to measure something that CAN be written down by numbers. D is the only answer choice that fits the definition of quantitive data. The answer is D: volume.

6 0

3 years ago

A 14.0 gauge copper wire of diameter 1.628 mmmm carries a current of 12.0 mAmA . Part A What is the potential difference across

NARA [144]

Answer:

a) 2.063*10^-4

b) 1.75*10^-4

Explanation:

Given that: d= 1.628 mm = 1.628 x 10-3 I= 12 mA = 12.0 x 10-8 A The Cross-sectional area of the wire is:

$A=\frac{\pi }{4}d^{2} \\=\frac{\pi }{4}*(1.628*10^-3 m)^2\\=2.082*10^-6 m^2\\$

a) <em>The Potential difference across a 2.00 in length of a 14-gauge copper </em>

L= 2.00 m

From Table Copper Resistivity $p$ = 1.72 x 10-8 S1 • m The Resistance of the Copper wire is:

$R=\frac{pL}{A}$

=0.0165Ω

The Potential difference across the copper wire is:

V=IR

=2.063*10^-4

b) The Potential difference if the wire were made of Silver: From Table: Silver Resistivity p= 1.47 x 10-8 S1 • m

The Resistance of the Silver wire is:

$R=\frac{pL}{A}$

=0.014Ω

The Potential difference across the Silver wire is:

V=IR

=1.75*10^-4

4 0

3 years ago