1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
larisa [96]
3 years ago
8

A projectile is launched at an angle of 30 and lands 20 s later at the same height as it was launched. (a) What is the initial s

peed of the projectile? (b) What is the maximum altitude? (c) What is the range? (d) Calculate the displacement from the point of launch to the position on its trajectory at 15 s.
Physics
1 answer:
Pavlova-9 [17]3 years ago
6 0

Answer:

(a) 196 m/s

(b) 490 m

(c) 3394.82 m

(d) 2572.5 m

Explanation:

First of all, let us know one thing. When an object is thrown in the air, it experiences two forces acting in two different directions, one in the horizontal direction called air resistance and the second in the vertically downward direction due to its weight. In most of the cases, while solving numerical problems, air resistance is neglected unless stated in the numerical problem. This means we can assume zero acceleration along the horizontal direction.

Now, while solving our numerical problem, we will discuss motion along two axes according to our convenience in the course of solving this problem.

<u>Given:</u>

  • Time of flight = t = 20 s
  • Angle of the initial velocity of projectile with the horizontal = \theta = 30^\circ

<u>Assume:</u>

  • Initial velocity of the projectile = u
  • R = Range of the projectile during the time of flight
  • H = maximum height of the projectile
  • D = displacement of the projectile from the initial position at t = 15 s

Let us assume that the position from where the projectile was projected lies at origin.

  • Initial horizontal velocity of the projectile = u\cos \theta
  • Initial horizontal velocity of the projectile = u\sin \theta

Part (a):

During the time of flight the displacement of the projectile along the vertical is zero as it comes to the same vertical height from where it was projected.

\therefore u\sin \theta t +\dfrac{1}{2}(-g)t^2\\\Rightarrow u\sin \theta t=\dfrac{1}{2}(g)t^2\\\Rightarrow u=\dfrac{gt^2}{2\sin \theta t}\\\Rightarrow u=\dfrac{9.8\times 20^2}{2\sin 30^\circ \times 20}\\\Rightarrow u=196\ m/s

Hence, the initial speed  of the projectile is 196 m/s.

Part (b):

For a projectile, the time take by it to reach its maximum height is equal to return from the maximum height to its initial height is the same.

So, time taken to reach its maximum height will be equal to 10 s.

And during the upward motion of this time interval, the distance travel along the vertical will give us maximum height.

\therefore H = u\sin \theta t +\dfrac{1}{2}(-g)t^2\\\Rightarrow H = 196\times \sin 30^\circ \times 10 + \dfrac{1}{2}\times(-9.8)\times 10^2\\ \Rightarrow H =490\ m

Hence, the maximum altitude is 490 m.

Part (c):

Range is the horizontal displacement of the projectile from the initial position. As acceleration is zero along the horizontal, the projectile is in uniform motion along the horizontal direction.

So, the range is given by:

R = u\cos \theta t\\\Rightarrow R = 196\times \cos 30^\circ \times 20\\\Rightarrow R =3394.82\ m

Hence, the range of the projectile is 3394.82 m.

Part (d):

In order to calculate the displacement of the projectile from its initial position, we first will have to find out the height of the projectile and its range during 15 s.

\therefore h = u\sin \theta t +\dfrac{1}{2}(-g)t^2\\\Rightarrow h = 196\times \sin 30^\circ \times 15 + \dfrac{1}{2}\times(-9.8)\times 15^2\\ \Rightarrow h =367.5\ m\\r = u\cos \theta t\\\Rightarrow r = 196\times \cos 30^\circ \times 15\\\Rightarrow r =2546.11\ m\\\therefore D = \sqrt{r^2+h^2}\\\Rightarrow D = \sqrt{2546.11^2+367.5^2}\\\Rightarrow D =2572.5\ m

Hence, the displacement from the point of launch to the position on its trajectory at 15 s is 2572.5 m.

You might be interested in
HEY CAN ANYONE PLS ANSWER THESE QUESTION!!!!!
Pie

1. A model can come in many shapes, sizes, and styles.

✅

2. Models can help scientists communicate their ideas, understand processes, and make predictions.

✅

3. Thomson's experiments with cathode ray tubes showed that all atoms contain tiny negatively charged subatomic particles or electrons.

✅

4. The plum pudding model has electrons surrounded by a volume of positive charge

✅

5. Electrons are kept in the orbit around the nucleus by the electromagnetic         force.

IamSugarbee

5 0
3 years ago
ANSWER ASAP 50 POINTS
spin [16.1K]

Answer:It turns out the Venus flytrap is a power plant, capable of generating electrical signals. Each trap is actually a modified leaf: a hinged midrib, which would be the central vein of a more familiar leaf, joins the two lobes, which secrete a sweet sap to attract insects.

Explanation:The leaves of Venus' Flytrap open wide and on them are short, stiff hairs called trigger or sensitive hairs. When anything touches these hairs enough to bend them, the two lobes of the leaves snap shut trapping whatever is inside.

4 0
3 years ago
If the bond enthalpy for a C-H bond is 413 kJ, what will happen when the C-H bond is broken?
pentagon [3]

Explanation:

Bond Enthalpy : It is defined as amount of energy required to break a the particular bond in there gaseous state. It is also known as bond energy. It units are kJ/mol.

  • Breaking of a bond is an Endothermic process (energy absorbed from the surroundings).
  • Formation of bond is an Exothermic process (energy is released to the surroundings).

If the average bond enthalpy for a C-H bond is 413 kJ/mol, When the C-H bond breaks in which energy will be required ,which will be an endothermic reaction.

8 0
3 years ago
The near point of a person's eye is 71.4 cm. To see objects clearly at a distance of 24.0 cm, what should be the focal length an
yuradex [85]

Answer:

The focal length of the appropriate corrective lens is 35.71 cm.

The power of the appropriate corrective lens is 0.028 D.

Explanation:

The expression for the lens formula is as follows;

\frac{1}{f}=\frac{1}{u}+\frac{1}{v}

Here, f is the focal length, u is the object distance and v is the image distance.

It is given in the problem that the given lens is corrective lens. Then, it will form an upright and virtual image at the near point of person's eye. The near point of a person's eye is 71.4 cm. To see objects clearly at a distance of 24.0 cm, the corrective lens is used.

Put v= -71.4 cm and u= 24.0 cm in the above expression.

\frac{1}{f}=\frac{1}{24}+\frac{1}{-71.4}

\frac{1}{f}=0.028

f= 35.71 cm

Therefore, the focal length of the corrective lens is 35.71 cm.

The expression for the power of the lens is as follows;

p=\frac{1}{f}

Here, p is the power of the lens.

Put f= 35.71 cm.

p=\frac{1}{35.71}

p=0.028 D

Therefore, the power of the corrective lens is 0.028 D.

3 0
3 years ago
Which processes cause rocks to be exposed<br> at Earth's surface? SC.7..6.2
seropon [69]

Answer:

weathering

Explanation:

5 0
3 years ago
Other questions:
  • under what conditions would a scale record a weight for an object which is equal to the magnitude of the gravitational force on
    14·2 answers
  • A 150 g egg is dropped from 3.0 meters. The egg is moving at 4.4 m/s right before it hits the ground. The egg comes to a stop in
    12·1 answer
  • How many years does one mouth symbolize on the cosmic calendar
    8·1 answer
  • What are the signs of "Depression"?
    12·2 answers
  • A projectile is fired over level ground with an initial velocity that has a vertical component of 20 m/s and a horizontal compon
    13·1 answer
  • What is one of Kepler's laws of planetary motion?
    11·1 answer
  • A jogger accelerates from rest to 4.86 m/s in 2.43 s. A car accelerates from 20.6 to 32.7 m/s also in 2.43 s. (a) Find the magni
    6·1 answer
  • WILL VOTE MOST BRAINLIEST
    15·1 answer
  • What are the two key guides to drawing a circuit diagram​
    14·2 answers
  • A mnemonic device in which phrases or poems use the first letter of each word to help a person remember the information is an ex
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!