Advertisements
Advertisements
प्रश्न
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. If he heads in a direction making an angle θ with the flow, find the time he takes to cross the river.
Advertisements
उत्तर
Given:
Width of the river = 500 m
Rate of flow of the river = 5 km/h
Swimmer's speed with respect to water = 3 km/h
As per the question, the swimmer heads in a direction making an angle θ with the flow.
We know that the vertical component of velocity 3 sin θ takes him to the opposite side of the river.
Distance to be travelled = 0.5 km
Vertical component of velocity = 3 sin θ km/h
Thus, we have:
\[\text{ Time }= \frac{\text{ Distance } }{\text{ Velocity }} = \frac{0 . 5}{3\sin\theta} h = \frac{500 \times 6}{5\sin\theta} = \frac{600}{\sin\theta} s\]
∴ Required time =\[\frac{10 \text{ minutes } }{\sin\theta}\]
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?
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.
At which point on its path a projectile has the smallest speed?
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 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 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 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 ?
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?
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 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 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 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.
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.
