Advertisements
Advertisements
Question
A man is sitting on the shore of a river. He is in the line of 1.0 m long boat and is 5.5 m away from the centre of the boat. He wishes to throw an apple into the boat. If he can throw the apple only with a speed of 10 m/s, find the minimum and maximum angles of projection for successful shot. Assume that the point of projection and the edge of the boat are in the same horizontal level.
Advertisements
Solution
Given:
Length of the boat = 1.0 m
Distance between the man and the centre of the boat (R) = 5.5 m
Initial speed (u) of throwing the apple by the man = 10 m/s
Acceleration due to gravity (g) = 10 m/s2
We know that the horizontal range is given by
R = `(u^2 sin 2alpha)/g`
⇒ `5 = ((10)^2 sin 2 alpha)/10`
⇒ `sin 2 alpha = 1/2`
⇒ α = 15° or 75°
Similarly, for the endpoint of the boat, i.e., point C, we have:
Horizontal range (R) = 6 m
R = `(u^2 sin 2alpha)/g`
⇒ `6 = ((10)^2 sin 2 alpha)/10`
⇒ `sin 2 alpha = 3/5`
⇒ α = 18° or 71°
For a successful shot, the angle of projection α with an initial speed of 10 m/s may vary from 15° to 18° or from 71° to 75°. The minimum angle is 15°, and the maximum angle is 75°, but there is an interval of 53° for which the successful shot is not allowed. We can show this by putting the successive value of α from 15° to 75°.
APPEARS IN
RELATED QUESTIONS
A car moving along a straight highway with a speed of 126 km h–1 is brought to a stop within a distance of 200 m. What is the retardation of the car (assumed uniform), and how long does it take for the car to stop?
A three-wheeler starts from rest, accelerates uniformly with 1 m s–2 on a straight road for 10 s, and then moves with uniform velocity. Plot the distance covered by the vehicle during the nth second (n = 1,2,3….) versus n. What do you expect this plot to be during accelerated motion: a straight line or a parabola?
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 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 maximum height.
A ball is projected vertically upward with a speed of 50 m/s. Find the time to reach the maximum height .
A ball is dropped from a balloon going up at a speed of 7 m/s. If the balloon was at a height 60 m at the time of dropping the ball, how long will the ball take in reaching the ground?
A stone is thrown vertically upward with a speed of 28 m/s. Find the maximum height reached by the stone.
A stone is thrown vertically upward with a speed of 28 m/s.Find its velocity one second before it reaches the maximum height.
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)?
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.
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 boy standing on a long railroad car throws a ball straight upwards. The car is moving on the horizontal road with an acceleration of 1 m/s2 and the projection velocity in the vertical direction is 9.8 m/s. How far behind the boy will the ball fall on the car?
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.
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.
