हिंदी
कर्नाटक बोर्ड पी.यू.सी.पीयूसी विज्ञान कक्षा ११

Find the Average Velocity of a Projectile Between the Instants It Crosses Half the Maximum Height. It is Projected with a Speed U at an Angle θ with the Horizontal.

Advertisements
Advertisements

प्रश्न

Find the average velocity of a projectile between the instants it crosses half the maximum height. It is projected with a speed u at an angle θ with the horizontal.

 
टिप्पणी लिखिए
Advertisements

उत्तर

Given:
Initial velocity of the projectile = u
Angle of projection = θ
To find: Average velocity of the projectile
Average velocity 

\[= \frac{ \text{ Change in displacement }}{\text{ Time } }\]
Consider the projectile motion in the figure given below.

By the symmetry of figure, it can be said that the line joining points A and B is horizontal.
So, there will be no effect of the vertical component of velocity of the projectile during displacement AB.
We know that the projectile moves at a constant velocity u cos θ in horizontal direction.
Hence, the average velocity of the projectile is u cos θ.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Rest and Motion: Kinematics - Exercise [पृष्ठ ५३]

APPEARS IN

एचसी वर्मा Concepts of Physics Volume 1 and 2 [English]
अध्याय 3 Rest and Motion: Kinematics
Exercise | Q 39 | पृष्ठ ५३

संबंधित प्रश्न

A player throws a ball upwards with an initial speed of 29.4 m s–1.

  1. What is the direction of acceleration during the upward motion of the ball?
  2. What are the velocity and acceleration of the ball at the highest point of its motion?
  3. Choose the x = 0 m and t = 0 s to be the location and time of the ball at its highest point, vertically downward direction to be the positive direction of x-axis, and give the signs of position, velocity and acceleration of the ball during its upward and downward motion.
  4. To what height does the ball rise and after how long does the ball return to the player’s hands? (Take g = 9.8 m s–2 and neglect air resistance).

The following figure gives the x-t plot of a particle executing one-dimensional simple harmonic motion. Give the signs of position, velocity and acceleration variables of the particle at t = 0.3 s, 1.2 s, – 1.2 s.


A boy standing on a stationary lift (open from above) throws a ball upwards with the maximum initial speed he can, equal to 49 m/s. How much time does the ball take to return to his hands? If the lift starts moving up with a uniform speed of 5 m/s and the boy again throws the ball up with the maximum speed he can, how long does the ball take to return to his hands?


In a projectile motion the velocity 


A train starts from rest and moves with a constant acceleration of 2.0 m/s2 for half a minute. The brakes are then applied and the train comes to rest in one minute. Find the total distance moved by the train.


A particle starting from rest moves with constant acceleration. If it takes 5.0 s to reach the speed 18.0 km/h find the average velocity during this period .


A stone is thrown vertically upward with a speed of 28 m/s. change if the initial speed is more than 28 m/s such as 40 m/s or 80 m/s ?


A healthy youngman standing at a distance of 7 m from a 11.8 m high building sees a kid slipping from the top floor. With what speed (assumed uniform) should he run to catch the kid at the arms height (1.8 m)?


A ball is dropped from a height. If it takes 0.200 s to cross the last 6.00 m before hitting the ground, find the height from which it was dropped. Take g = 10 m/s2.

 

An elevator is descending with uniform acceleration. To measure the acceleration, a person in the elevator drops a coin at the moment the elevator starts. The coin is 6 ft above the floor of the elevator at the time it is dropped. The person observes that the coin strikes the floor in 1 second. Calculate from these data the acceleration of the elevator.


A ball is thrown horizontally from a point 100 m above the ground with a speed of 20 m/s. Find the velocity (direction and magnitude) with which it strikes the ground. 


A popular game in Indian villages is goli which is played with small glass balls called golis. The goli of one player is situated at a distance of 2.0 m from the goli of the second player. This second player has to project his goli by keeping the thumb of the left hand at the place of his goli, holding the goli between his two middle fingers and making the throw. If the projected goli hits the goli of the first player, the second player wins. If the height from which the goli is projected is 19.6 cm from the ground and the goli is to be projected horizontally, with what speed should it be projected so that it directly hits the stationery goli without falling on the ground earlier? 


In the following figure shows a 11.7 ft wide ditch with the approach roads at an angle of 15° with the horizontal. With what minimum speed should a motorbike be moving on the road so that it safely crosses the ditch?

Assume that the length of the bike is 5 ft, and it leaves the road when the front part runs out of the approach road.


A boy standing on a long railroad car throws a ball straight upwards. The car is moving on the horizontal road with an acceleration of 1 m/s2 and the projection velocity in the vertical direction is 9.8 m/s. How far behind the boy will the ball fall on the car?

 

A person is standing on a truck moving with a constant velocity of 14.7 m/s on a horizontal road. The man throws a ball in such a way that it returns to the truck after the truck has moved 58.8 m. Find the speed and the angle of projection  as seen from the road. 


A river 400 m wide is flowing at a rate of 2.0 m/s. A boat is sailing at a velocity of 10 m/s with respect to the water, in a direction perpendicular to the river. Find the time taken by the boat to reach the opposite bank. 


A swimmer wishes to cross a 500 m wide river flowing at 5 km/h. His speed with respect to water is 3 km/h.  Find the shortest possible time to cross the river.


A ball is dropped from a building of height 45 m. Simultaneously another ball is thrown up with a speed 40 m/s. Calculate the relative speed of the balls as a function of time.


It is a common observation that rain clouds can be at about a kilometre altitude above the ground.

  1. If a rain drop falls from such a height freely under gravity, what will be its speed? Also calculate in km/h. ( g = 10 m/s2)
  2. A typical rain drop is about 4mm diameter. Momentum is mass x speed in magnitude. Estimate its momentum when it hits ground.
  3. Estimate the time required to flatten the drop.
  4. Rate of change of momentum is force. Estimate how much force such a drop would exert on you.
  5. Estimate the order of magnitude force on umbrella. Typical lateral separation between two rain drops is 5 cm.

(Assume that umbrella is circular and has a diameter of 1 m and cloth is not pierced through !!)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×