Advertisements
Advertisements
प्रश्न
A man can swim with a speed of 4.0 km/h in still water. How long does he take to cross a river 1.0 km wide if the river flows steadily at 3.0 km/h and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank?
उत्तर १
Hera, `vecV_m = 4 km h^(-1), vecv_r = 3 km h^(-1)`
OA = 1 km
Let t = time taken by man to reach the other bank
then `t = (OA)/v_m = 1/4 = 0.25 h`
Distance `AB = v_t xx t =3 xx 0.25 = 0.75 km.`
उत्तर २
Speed of the man, vm = 4 km/h
Width of the river = 1 km
Time taken to cross the river = `"Width of river"/"Speed of man"`
`=1/4h = 1/4 xx 60 = 15 min`
Speed of the river, vr = 3 km/h
Distance covered with flow of the river = vr × t
`= 3 xx 1/4 = 3/4` km
`=3/4 xx 1000 = 750 m`
APPEARS IN
संबंधित प्रश्न
An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at a ground observation point by the aircraft positions 10.0 s a part is 30°, what is the speed of the aircraft?
A car starts from rest and accelerates at 5 m/s2. At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t = 6 s? (Take g = 10 m/s2)
Two particles are projected in air with speed vo at angles θ1 and θ2 (both acute) to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then tick the right choices
- Angle of projection: q1 > q2
- Time of flight: T1 > T2
- Horizontal range: R1 > R2
- Total energy: U1 > U2
A particle slides down a frictionless parabolic (y = x2) track (A – B – C) starting from rest at point A (Figure). Point B is at the vertex of parabola and point C is at a height less than that of point A. After C, the particle moves freely in air as a projectile. If the particle reaches highest point at P, then
A particle is projected in air at some angle to the horizontal, moves along parabola as shown in figure, where x and y indicate horizontal and vertical directions, respectively. Show in the diagram, direction of velocity and acceleration at points A, B and C.
A boy travelling in an open car moving on a levelled road with constant speed tosses a ball vertically up in the air and catches it back. Sketch the motion of the ball as observed by a boy standing on the footpath. Give explanation to support your diagram.
A boy throws a ball in air at 60° to the horizontal along a road with a speed of 10 m/s (36 km/h). Another boy sitting in a passing by car observes the ball. Sketch the motion of the ball as observed by the boy in the car, if car has a speed of (18 km/h). Give explanation to support your diagram.
A girl riding a bicycle with a speed of 5 m/s towards north direction, observes rain falling vertically down. If she increases her speed to 10 m/s, rain appears to meet her at 45° to the vertical. What is the speed of the rain? In what direction does rain fall as observed by a ground based observer?
A cricket fielder can throw the cricket ball with a speed vo. If he throws the ball while running with speed u at an angle θ to the horizontal, find
- the effective angle to the horizontal at which the ball is projected in air as seen by a spectator.
- what will be time of flight?
- what is the distance (horizontal range) from the point of projection at which the ball will land?
- find θ at which he should throw the ball that would maximise the horizontal range as found in (iii).
- how does θ for maximum range change if u > vo, u = vo, u < vo?
- how does θ in (v) compare with that for u = 0 (i.e.45)?
An object is projected in the air with initial velocity u at an angle θ. The projectile motion is such that the horizontal range R, is maximum.
Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be ______ degree.
