Which of the following is/ are independent of the angle of projection of a projectile :
(a) time of flight
(b) maximum height reached
(c) acceleration of projectile
(d) horizontal component of velocity
The time of flight is determined by considering vertical motion. It means that time of flight is dependent on speed and the angle of projection.
Maximum height is also determined, considering vertical motion. As such, maximum height also depends on the angle of projection.
Horizontal component, being component of velocity, depends on the angle of projection.
It is only the acceleration of projectile, which is equal to acceleration due to gravity and is, therefore, independent of the angle of projection. Hence, option (c) is correct.
The velocity of a projectile during its flight at an elevation of 8 m from the ground is 3
i - 5
j in the coordinate system, where x and y directions represent horizontal and vertical directions respectively. The maximum height attained (H) by the particle is :
We note that vertical component is negative, meaning that projectile is moving towards the ground. The vertical component of velocity 8 m above the ground is
The vertical displacement (y) from the maximum height to the point 8 m above the ground as shown in the figure can be obtained, using equation of motion.
Considering the point under consideration as origin and upward direction as positive direction.
Thus, the maximum height, H, attained by the projectile is :
A projectile is thrown with a given speed so as to cover maximum range (R).
If "H" be the maximum height attained during the throw, then the range "R" is equal to :
The projectile covers maximum range when angle of projection is equal to 45°. The maximum range "R" is given by :
On the other hand, the maximum height attained by the projectile for angle of projection, 45°, is :
Comparing expressions of range and maximum height, we have :
The speed of a projectile at maximum height is half its speed of projection, "u".
The horizontal range of the projectile is :
The horizontal range of the projectile is given as :
In order to evaluate this expression, we need to know the angle of projection. Now, the initial part of the question says that the speed of a projectile at maximum height is half its speed of projection, "u". However, we know that speed of the projectile at the maximum height is equal to the horizontal component of projection velocity,
Let "
” and “
” be the times of flights of a projectile for projections at two complimentary angles for which horizontal range is "R". The product of times of flight, "
”, is equal to :
Here, we are required to find the product of times of flight. Let "
" and "
" be two angles of projections. The times of flight are given as :
A projectile is projected with a speed "u" at an angle "
" from the horizontal. The magnitude of average velocity between projection and the time, when projectile reaches the maximum height.
The magnitude of average velocity is given as :
Now the displacement here is OA as shown in the figure. From right angle triangle OAC,
Hence, magnitude of average velocity is :
Substituting expression for each of the terms, we have :
A projectile is projected at an angle "
" from the horizon. The tangent of angle of elevation of the highest point as seen from the position of projection is :
The angle of elevation of the highest point "
" is shown in the figure. Clearly,
Putting expressions of the maximum height and range of the flight, we have :
In a firing range, shots are taken at different angles and in different directions. If the speed of the bullets is "u", then find the area in which bullets can spread.
The bullets can spread around in a circular area of radius equal to maximum horizontal range. The maximum horizontal range is given for angle of projection of 45°.
The circular area corresponding to the radius equal to maximum horizontal range is given as :
Check the module titled "
Features of projectile motion (application) to work out more problems.
Questions & Answers
Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you.
Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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