^Oblique projectile from ground Suppose a body is projected from the ground from point O at an angel q with the horizontal and with the velocity u. Let at time t the projectile is at point P where its velocity is v directed at angle b to the horizontal. 1 Using trigonometry x & y […]
^Horizontal projectiles Suppose a body is projected from some height from point O horizontally with the velocity u. Let at time ‘t’ the projectile is at point P (x, -y) where its velocity is v directed at angle b to the horizontal. For the motion O to P along x & y axis we can […]
^For a body just released from a height If a body is dropped from a height h, 1. it reaches the ground with speed [using v – s relation] 2. The time taken by it to reach the ground is [using s – t relation]
^Projectile thrown straight up Suppose a body is projected upwards from the ground and with the velocity u. The characteristics of motion of such a body are as follows. The maximum height attained Time taken to go up (ascent) = Time taken to come down (descent) Time of flight For an object thrown straight upwards […]
^What is a projectile A projectiles is any object moving under the influence of gravity. There are several ways to throw a projectile, vertically up, vertically down, horizontally, at some angle up, at some angle down etc. Object is thrown → means initial speed non zero. Object is dropped → means initial speed zero.Assumptions Following […]
^Trajectory Path traveled by a point particle is called trajectory (or locus). It is straight (if a & v are collinear) & curved otherwise.
^Moving upstream & downstream In such a case the boat is not crossing the river, rather it moves along or opposite to stream. Distance covered in the opposite to direction of river current is called upstream & that covered in the direction of river current downstream. i.e. for a particular distance the still water time […]
^Condition for shortest distance As the shortest distance between the two points is their perpendicular distance, thus he must reach exactly opposite bank as shown. From the diagram one can write
^Condition for shortest time At a = 00 the time taken to cross the river will be minimum & given by This is the case when the boat w.r.t. water is moved along the normal to river current as shown below. From the diagram one can write
^Crossing a river Suppose a person start rowing his boat from point O with velocity vbr (w.r.t. river i.e. without considering the effect of water) towards point S in order to cross a river of width ‘w’ flowing at a speed ‘vr’ towards x axis. Let under the effect of river current boat has net […]
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