Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let the speeds of the two balls (1 and 2) be v1 and v2 where
If v1 = 2v, v2 = v
If y1 and y2 and the distance covered by balls 1 and 2, respectively before coming to rest then
`y_1 = v_1^2/(2g) = (4v^2)/(2g)` and `y_2 = (v_2^2)/(2g) = v^2/(2g)`
Since, `y_1 - y_2 = 15 m (4v^2)/(2g) - v^2/(2g)` = 15 m or `(3v^2)/(2g)` = 15 m
or `v^2 = sqrt(5m xx (2 xx 10))` m/s2
or v = 10 m/s
Clearly, v1 = 20 m/s and v2 = 10 m/s
As `y_1 = v_1^2/(2g) = (20 m)^2/(2 xx 10 m 15)` = 20 m
`y_2 - y_1 - 15` m = 5 m
It t2 is the time taken by the ball 2 toner a distance of 5 m, then from `y_2 = v_2^t - 1/2 "gt"_2^2`
5 = `10t_2 - 5t_2^2` or `t_2^2 - 2t_2 + 1` = 0
Where t2 = 15
Since t1 (time taken by ball 1 to cover the distance of 20 m) is 2s, the time interval between the two throws
= t1 – t2
= 2s – 1s
= 1s
APPEARS IN
संबंधित प्रश्न
A ball is dropped from a height of 90 m on a floor. At each collision with the floor, the ball loses one tenth of its speed. Plot the speed-time graph of its motion between t = 0 to 12 s.
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 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 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 going with speed 350 m/s enters a concrete wall and penetrates a distance of 5.0 cm before coming to rest. Find the deceleration.
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 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.
Complete the following table:
| Car Model | Driver X Reaction time 0.20 s |
Driver Y Reaction time 0.30 s |
| A (deceleration on hard braking = 6.0 m/s2) | Speed = 54 km/h Braking distance a = ............ Total stopping distance b = ............ |
Speed = 72 km/h Braking distance c = ........... Total stopping distance d = ............ |
| B (deceleration on hard braking = 7.5 m/s2) | Speed = 54 km/h Breaking distance e = ........... Total stopping distance f = ............ |
Speed 72 km/h Braking distance g = ............. Total stopping distance h = ............ |
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 person standing on the top of a cliff 171 ft high has to throw a packet to his friend standing on the ground 228 ft horizontally away. If he throws the packet directly aiming at the friend with a speed of 15.0 ft/s, how short will the packet fall?
A staircase contains three steps each 10 cm high and 20 cm wide (in the following figure). What should be the minimum horizontal velocity of a ball rolling of the uppermost plane so as to hit directly the lowest plane?
Consider the situation of the previous problem. The man has to reach the other shore at the point directly opposite to his starting point. If he reaches the other shore somewhere else, he has to walk down to this point. Find the minimum distance that he has to walk.
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 direction in which the pilot should head the plane to reach the point B.
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?
Six particles situated at the corner of a regular hexagon of side a move at a constant speed v. Each particle maintains a direction towards the particle at the next corner. Calculate the time the particles will take to meet each other.
