Advertisements
Advertisements
Question
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.
Advertisements
Solution
In motion under gravity, if the ball is released or dropped that means its initial velocity is zero. In this problem, as the ball is dropped, its initial velocity will be taken as zero. We will apply kinematic equations.
According to the problem, for the ball dropped from the building, u1 = 0, u2 = 40 m/s
The velocity of the ball after time t,
v1 = u1 – gt
v1 = – gt
And for another ball which is thrown upward,
u2 = 40 m/s
The velocity of the ball after time t,
v2 = u2 – gt = (40 – gt)
∴ The relative velocity of one ball w.r.t another ball is
v12 = v1 – v2 = – gt – [– 40 – gt]
v12 = v1 – v2 = – gt + 40 + gt = 40 m/s
APPEARS IN
RELATED QUESTIONS
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 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 .
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 position(s) of the train at half the maximum speed.
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 police jeep is chasing a culprit going on a motorbike. The motorbike crosses a turning at a speed of 72 km/h. The jeep follows it at a speed of 90 km/h, crossing the turning ten seconds later than the bike. Assuming that they travel at constant speeds, how far from the turning will the jeep catch up with the bike?
A ball is projected vertically upward with a speed of 50 m/s. Find the time to reach the maximum height .
A stone is thrown vertically upward with a speed of 28 m/s. Find the maximum height reached by the stone.
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?
In a soccer practice session the football is kept at the centre of the filed 40 yards from the 10 ft high goalposts. A goal is attempted by kicking the football at a speed of 64 ft/s at an angle of 45° to the horizontal. Will the ball reach the goal post?
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 ball is projected from a point on the floor with a speed of 15 m/s at an angle of 60° with the horizontal. Will it hit a vertical wall 5 m away from the point of projection and perpendicular to the plane of projection without hitting the floor? Will the answer differ if the wall is 22 m away?
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?
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 truck .
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.
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.
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.
