Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
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 player throws a ball upwards with an initial speed of 29.4 m s–1.
- What is the direction of acceleration during the upward motion of the ball?
- What are the velocity and acceleration of the ball at the highest point of its motion?
- Choose the x = 0 m and t = 0 s to be the location and time of the ball at its highest point, vertically downward direction to be the positive direction of x-axis, and give the signs of position, velocity and acceleration of the ball during its upward and downward motion.
- To what height does the ball rise and after how long does the ball return to the player’s hands? (Take g = 9.8 m s–2 and neglect air resistance).
Two stones are thrown up simultaneously from the edge of a cliff 200 m high with initial speeds of 15 m/s and 30 m/s. Verify that the graph shown in Fig. 3.27 correctly represents the time variation of the relative position of the second stone with respect to the first. Neglect air resistance and assume that the stones do not rebound after hitting the ground. Take g = 10 m/s2. Give the equations for the linear and curved parts of the plot.
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 ball is projected vertically upward with a speed of 50 m/s. Find the time to reach the maximum height .
A ball is projected vertically upward with a speed of 50 m/s. Find the speed at half the maximum height. Take g = 10 m/s2.
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 ?
A healthy youngman standing at a distance of 7 m from a 11.8 m high building sees a kid slipping from the top floor. With what speed (assumed uniform) should he run to catch the kid at the arms height (1.8 m)?
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 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.
A popular game in Indian villages is goli which is played with small glass balls called golis. The goli of one player is situated at a distance of 2.0 m from the goli of the second player. This second player has to project his goli by keeping the thumb of the left hand at the place of his goli, holding the goli between his two middle fingers and making the throw. If the projected goli hits the goli of the first player, the second player wins. If the height from which the goli is projected is 19.6 cm from the ground and the goli is to be projected horizontally, with what speed should it be projected so that it directly hits the stationery goli without falling on the ground earlier?
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 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?
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.
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.
Two friends A and B are standing a distance x apart in an open field and wind is blowing from A to B. A beat a drum and B hears the sound t1 time after he sees the event. A and B interchange their positions and the experiment is repeated. This time B hears the drum timer after he sees the event. Calculate the velocity of sound in still air v and the velocity of wind u. Neglect the time light takes in travelling between the friends.
