where the line cuts the y-axis. 56: To a man walking at the rate of 3 km/h the rain appears to fall vertically. The NCERT Class 11th Physics textbooks are well known for it’s updated and thoroughly revised syllabus. The situation when the man runs is shown in the figure, Here  = velocity of the rain with respect to the ground. Their movement in two component directions should be synchronized so that they are at the same position at a particular given time. 49: Two ships A and B are 10 km apart on a line running south to north. (a) Time of Flight : ⇒ - H = (0)T -  ⇒ T = (b) Final Velocity when body reaches the ground : ⇒  - 0 = 2 (-g) (-H) ⇒ vf = Ex. (ii) If a body is dropped from a height h above the ground. Let T be its time of flight. ⇒ A = Ex. 52: A boat moves relative to water with a velocity v and river is flowing with 2v. The ball attains a maximum height Hmax. 33: A body is projected with a velocity of 30 ms-1 at an angle of 30° with the vertical. For example, my height is five feet and six inches while my wife's height is five feet and four inches. Thus, the given problem can be simplified as : A is at rest and B is moving with  in the direction shown in figure. Ship A farther north is streaming west at 20 km/h and ship B is streaming north at 20km/h. He finds that raindrops are hitting his head vertically. Hmax is same for all three particle A, B, C. ⇒ uxC > uxB > uxA  ⇒ uA < uB< uC(C) Coordinate of a particle after a given time t : Particle reach at a point p after time t then. (a) Given, that vbr = 4 km/h and vr = 2 km/h. or nh = 0  =  or n = 4.3 Projectile at an Angle q from Height h :Consider the projectile as shown in the adjacent figure. (F) Instantaneous speed and instantaneous velocity :Instantaneous speed is also defined exactly like average speed i.e. Let us choose the x and y directions along OB and OA respectively. Mathematically. Kinematics Formulas. The concepts should be clear which will help in faster learning. 21: A balloon is ascending at the rate of 9.8 ms-1 at a height of 39.2 m above the ground when a food packet is dropped from the balloon. (6) Body is at rest initially. Reaction time is the time a person takes to observe, think and act. At the same time a second particle B is projected in opposite direction with initial speed of 50 m/s from a point at a distance of 100 m from A. (vi) For t > t1 velocity of B is greater than velocity of A. This is vy = u sin θ - gt, and y = u sin θ t - Ex. At t = t0 the body comes to rest instantaneously and reverses its direction of motion and then continues to move with decreasing velocity or increasing speed. v = u + gt = 9.8 - 9.8 × 4 = - 29.4 ms-1. (4)  Body starts its motion with initial velocity v0 and continues to move with its velocity increasing at a constant rate i.e. 59: Two projectiles are projected simultaneously from two towers as shown in figure. Refer to figure. 58: Two projectile are projected simultaneously from a point on the ground "O" and an elevated position "A" respectively as shonw in the figure. 38: A body is thrown horizontally from the top of a tower and strikes the ground after three seconds at an angle of 45° with the horizontal. Therefore velocity of B is greater than velocity of A. 12 to 20 in Ex.II5. y = 4 x2 + 3x           Average velocity & instantaneous velocity from position vs time graph : Average velocity from t1 to t2, when t2 approaches t1 point B approaches point A and the chord AB becomes tangent to the curve. 16: What is the maximum separation between car and scooter ?Sol. 11 th Class; 12 th Class; Complete Course (11 th & 12 th Class) Algebra; Calculus; Trigonometry; Coordinate Geometry; Statistics; Physics. (at top most point) and again increases in the negative direction.Ex. If R is the range of the particle, then from the figure we have. The horizontal distance covered by the body in time t is, The vertical distance travelled by the body in time t is given by. It becomes zero after body reverse its direction of motion and continues to move with decreasing velocity or increasing speed. Considering verticlly downward motion of the body, y = uyt + = 0 × 3 +  ×9.8 × (3)2 = 44.1 m [ Initial vertical velocity, uy = 0], As the resultant velocity u makes an angle of 45° with the horizontal, so. This is the direction of the velocity of raindrops with respect to the ground. This article will explain the Physics kinematics formulas with examples. Therefore, the pilot should steer in a direction at an angle of (45° +α) or 75° from north towards east. (4) Body starts from rest from x = x0 and moves away from origin with increasing velocity or ve acceleration. Its acceleration is positive for whole of its motion. Physics is all around you when you think about it. (C) 2020 by Dimension Academy Junior College, Tezpur. (i) Distance = length of path of particle =  = πR, (ii) Displacement = minimum distance between initial and final point. * Distance > Magnitude of displacement. The distance travelled by scooter in 10 sec. (b) If width of the river is 4 km, how long will the man take to cross the river, with the condition in part (a)? A wind of  km/h is blowing from the south. Find the direction he must steer and time of his journey if AB = 1000 km.Sol. Learning the important concepts is very important for every student to get better marks in examinations. Acceleration of both the particles is g downwards. = u cos a T +Ex. Take the point of projection as the origin the X and Y-axes as shown in figure. Now, let us derive the expressions for time of flight (T) and range (R) along the plane. Take a rule and ask your friend to drop it vertically through the gap between your thumb and forefinger. 6: If velocity is depend on time such that v = 4 - 2t. (as θ = 90º). Distance covered in 0.5 sec, with a uniform speed is, Now car begins to move with a retardation of 8ms-2. 37: A particle is projected over a triangle from one end of a horizontal base and grazing the vertex falls on the other end of the base. How high did it go and with what velocity was it thrown ? * It can never decrease with time. In the nutshell, their times of flight should be equal. If the direction of motion at the instant when the particle hits the plane be perpendicular to the plane, then the velocity at that instant parallel to the plane must be zero. (A) 30°(B) 60°(C) 90°(D) 120°Sol. When the man is at rest with respect to the ground, the rain comes to him at an angle 30° with the vertical. Equation (2) is another form of trajectory equation of projectile.Ex. 2y = 3x + 2 ⇒ y =, ⇒ The line will pass through (0, 1)Ex. (g = 10 m/s2), Relative acceleration between the two is zero as . 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