Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given:
Distance travelled by the ball in 0.200 seconds = 6 m
Let:
Time, t = 0.200 s
Distance, s = 6 m
a = g = 10 m/s2 (Acceleration due to gravity)
Using the equation of motion, we get:
\[s = ut + \frac{1}{2}a t^2 \]
\[6 = u\left( 0 . 2 \right) + \frac{1}{2} \times 10 \times 0 . 04\]
\[ \Rightarrow u = \frac{5 . 8}{0 . 2} = 29 \text{ m } /s\]
Let h be the height from which the ball is dropped.
We have:
u = 0 and v = 29 m/s
Now,
\[h = \frac{v^2 - u^2}{2a}\]
\[\Rightarrow h = \frac{{29}^2 - 0^2}{2 \times 10} = \frac{29 \times 29}{20} = 42 . 05 \text{ m } \]
∴ Total height = 42.05 + 6 = 48.05 m ≈ 48 m
APPEARS IN
संबंधित प्रश्न
Two trains A and B of length 400 m each are moving on two parallel tracks with a uniform speed of 72 km h–1 in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by 1 m/s2. If after 50 s, the guard of B just brushes past the driver of A, what was the original distance between them?
The velocity of a particle is towards west at an instant. Its acceleration is not towards west, not towards east, not towards north and towards south. Give an example of this type of motion .
Two bullets are fired simultaneously, horizontally and with different speeds from the same place. Which bullet will hit he ground first?
A person travelling at 43.2 km/h applies the brake giving a deceleration of 6.0 m/s2 to his scooter. How far will it travel before stopping?
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 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 particle starting from rest moves with constant acceleration. If it takes 5.0 s to reach the speed 18.0 km/h find the distance travelled by the particle during this period.
A car travelling at 60 km/h overtakes another car travelling at 42 km/h. Assuming each car to be 5.0 m long, find the time taken during the overtake and the total road distance used for the overtake.
A stone is thrown vertically upward with a speed of 28 m/s.Find its velocity one second before it reaches the maximum height.
An NCC parade is going at a uniform speed of 6 km/h through a place under a berry tree on which a bird is sitting at a height of 12.1 m. At a particular instant the bird drops a berry. Which cadet (give the distance from the tree at the instant) will receive the berry on his uniform?
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 maximum height reached .
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.
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.
The benches of a gallery in a cricket stadium are 1 m wide and 1 m high. A batsman strikes the ball at a level one metre above the ground and hits a mammoth sixer. The ball starts at 35 m/s at an angle of 53° with the horizontal. The benches are perpendicular to the plane of motion and the first bench is 110 m from the batsman. On which bench will the ball hit?
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.
An aeroplane has to go from a point A to another point B, 500 km away due 30° east of north. A wind is blowing due north at a speed of 20 m/s. The air-speed of the plane is 150 m/s. Find the time taken by the plane to go from A to B.
Suppose A and B in the previous problem change their positions in such a way that the line joining them becomes perpendicular to the direction of wind while maintaining the separation x. What will be the time B finds between seeing and hearing the drum beating by A?
A man is standing on top of a building 100 m high. He throws two balls vertically, one at t = 0 and other after a time interval (less than 2 seconds). The later ball is thrown at a velocity of half the first. The vertical gap between first and second ball is +15 m at t = 2 s. The gap is found to remain constant. Calculate the velocity with which the balls were thrown and the exact time interval between their throw.
