Advertisements
Advertisements
प्रश्न
A bomb is dropped from a plane flying horizontally with uniform speed. Show that the bomb will explode vertically below the plane. Is the statement true if the plane flies with uniform speed but not horizontally?
Advertisements
उत्तर
The plane is flying horizontally with a uniform speed. Therefore, the bomb also has the same speed.
Let the speed of the plane be represented by u.
Now, let t be the time taken by the bomb to reach the ground.
Distance travelled by the bomb in horizontal direction = ut
Both the plane and bomb are travelling in the same direction.
Distance travelled by the plane in the same time = ut
Hence, the bomb will explode vertically below the plane.
When the plane is flying with a uniform speed but not horizontally:
Let us consider it will make an angle of projection θ along the horizontal direction.
So, both the plane and the bomb will be flying with the same angle of projection.
Therefore, both will have the same horizontal speed u cos θ, where u is the initial speed of the plane and the bomb.
When the bomb is released, the time taken by the bomb to reach the ground is t.
The distance travelled by the bomb and the plane will be u cos θt.
Hence, again the bomb will explode vertically below the plane.
(i) During the motion of bomb, its horizontal velocity u remains constant and is the same as that of the plane at every point of its path.
Let the bomb reach the ground in time t.
Distance travelled in horizontal direction by the bomb = ut
Distance travelled in horizontal direction by the bomb is the same as that travelled by the plane.
So, the bomb will explode vertically below the plane.
(ii) Let the plane move making an angle α with the horizontal.
Horizontal distance for both the bomb and the plane = u cos αt'
t' = Time taken by the bomb to reach the ground
So, in this case also, the bomb will explode vertically below the plane.
APPEARS IN
संबंधित प्रश्न
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 three-wheeler starts from rest, accelerates uniformly with 1 m s–2 on a straight road for 10 s, and then moves with uniform velocity. Plot the distance covered by the vehicle during the nth second (n = 1,2,3….) versus n. What do you expect this plot to be during accelerated motion: a straight line or a parabola?
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?
Two bullets are fired simultaneously, horizontally and with different speeds from the same place. Which bullet will hit he ground first?
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 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 maximum speed attained by the train .
A bullet travelling with a velocity of 16 m/s penetrates a tree trunk and comes to rest in 0.4 m. Find the time taken during the retardation.
A driver takes 0.20 s to apply the brakes after he sees a need for it. This is called the reaction time of the driver. If he is driving a car at a speed of 54 km/h and the brakes cause a deceleration of 6.0 m/s2, find the distance travelled by the car after he sees the need to put the brakes on.
A stone is thrown vertically upward with a speed of 28 m/s. Find the maximum height reached by the stone.
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 horizontal distance it travels before reaching the ground .
A ball is thrown at a speed of 40 m/s at an angle of 60° with the horizontal. Find the range of the ball. Take g = 10 m/s2.
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.
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 man is sitting on the shore of a river. He is in the line of 1.0 m long boat and is 5.5 m away from the centre of the boat. He wishes to throw an apple into the boat. If he can throw the apple only with a speed of 10 m/s, find the minimum and maximum angles of projection for successful shot. Assume that the point of projection and the edge of the boat are in the same horizontal level.
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 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. How far from the point directly opposite to the starting point does the boat reach the opposite bank?
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.
