Based on the map, which area has a scarcity of fresh water?

The height (in meters) of a projectile shot vertically upward from a point 3 m above ground level with an initial velocity of 21

frutty [35]

Answer:

a) The velocity of the projectile at 2 seconds after launch is 1.9 meters per second. The velocity of the projectile at 4 seconds after launch is -17.7 meters per second.

b) The projectile reaches maximum height 2.192 seconds after launch.

c) The maximum height of the projectile is 26.584 meters above ground.

d) The projectile will hit the ground at 4.523 seconds after launch.

e) The velocity of the projectile right before hitting the ground in -22.871 meters per second.

Explanation:

Complete statement of problem is: The height (in meters) of a projectile shot vertically upward from a point 3 m above ground level with an initial velocity of 21.5 meters per second is $h(t) = 3+21.5\cdot t-4.9\cdot t^{2}$ after t seconds. (Round your answers to two decimal places.) (a) Find the velocity after 2 seconds and after 4 seconds, (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 hits the ground?

a) From Physics and Differential Calculus we remember that velocity is the first derivative of height. Hence, we need to differentiate the height function in time:

$v(t) = 21.5-9.8\cdot t$ (Eq. 1)

Where $v(t)$ is the velocity function, measured in meters per second.

Now we evaluate this function at given times:

t = 2 s.

$v(2) = 21.5-9.8\cdot (2)$

$v(2) = 1.9\,\frac{m}{s}$

The velocity of the projectile at 2 seconds after launch is 1.9 meters per second.

t = 4 s.

$v(4) = 21.5-9.8\cdot (4)$

$v(4) = -17.7\,\frac{m}{s}$

The velocity of the projectile at 4 seconds after launch is -17.7 meters per second.

b) Maximum height is reached when velocity of projectile is zero. We equalize velocity to zero and solve the expression for $t$ :

$21.5-9.81\cdot t = 0$

$t = 2.192\,s$

The projectile reaches maximum height 2.192 seconds after launch.

c) Maximum height is calculated by evaluating height function at the time found in b). That is:

$h(2.192) = 3+21.5\cdot (2.192)-4.9\cdot (2.192)^{2}$

$h (2.192) = 26.584\,m$

The maximum height of the projectile is 26.584 meters above ground.

d) In this case, we need to equalize the height function to zero and solve for $t$ . That is:

$3+21.5\cdot t-4.9\cdot t^{2} = 0$

Roots are found by means of Quadratic Formula:

$t_{1}\approx 4.523\,s$ and $t_{2}\approx -0.135\,s$

Only the first root offers a physically reasonable solution. Therefore, the projectile will hit the ground at 4.523 seconds after launch.

e) This can be found by evaluating velocity function at the time found in d):

$v(4.523) = 21.5-9.81\cdot (4.523)$

$v(4.523) = -22.871\,\frac{m}{s}$

The velocity of the projectile right before hitting the ground in -22.871 meters per second.

5 0

4 years ago

Use the data below to compute the gravitational force that the Sun exerts on Jupiter. (Use G = 6.67 x 10^-11 N · m²/kg².)

Mademuasel [1]

The gravitational force on two objects can be determined by the following equation:

$F=G\frac{m_{1}m_{2}}{r^2}$

Where G is the gravitational constant m1 is mass 1, m2 is the second mass nad r^2 is distance between these objects. Therefore, let m1 = mass of Sun 1.99x10^30 kg, m2= mass of Jupiter 1.90x10^27 kg, r is the average distance between the Sun and Jupiter 7.78x10^11 m. By plugging these values in we have:

$F=6.67x10^{-11}\frac{(1.99x10^{30})(1.90x10^{27})}{(7.78x10^{11})^2}$

$F=4.1665x10^{23}$

F=4.17x10^23 N

8 0

3 years ago

In 5 or more sentences, explain how you can make everyday count ?

IceJOKER [234]

You can make everyday count by accomplishing all the tasks you have for that day. Also you can try and find the positive throughout the day. Another thing you could do is eat a healthy meal. You can do a workout and that will make you feel better about your self. The last thing you can do is always have a good mindset about that day.

8 0

3 years ago

Explain why meteorologists compare new weather maps and weather maps that are 24 hours old

lawyer [7]

To see which way atmospheric conditions and meteorological phenomena are moving, and how fast.

Also to see whether they were correct yesterday.

3 0

4 years ago

What special component would you need to use in a thermostat so that it can respond to changes in temperature

stepan [7]

Answer:

A thermistor is an electrical device, a thermally sensitive semiconductor resistor, whose resistance changes in response to temperature. Thermistors are made in a variety of ways including thin films (SiC).

Explanation:

hope it helps

4 0

3 years ago