Q: At time t = 0 a small ball is projected from point A with a velocity of 60 m/s at 60° angle with horizontal. Neglecting atmospheric resistance the two times t1 and t2 when the velocity of the ball makes an angle of 45° with the horizontal x-axis .
(a) 2.19 s, 8.2 s
(b) 3.19 s, 9.2 s
(c) 2.12 s, 8.2 s
(d) 2.19 s, 10.2 s
Where , α = ±45° , θ = 60°
on putting α = ±45° , θ = 60° , get two values of t
Q: A body is projected obliquely from the ground such that its horizontal range is maximum. If the change in its linear momentum, as it moves from half the maximum height to maximum height, is P, the change in its linear momentum as it travels from the point of projection to the landing point on the ground will be
(b) √2 P
(d) 2√2 P
Sol: Maximum height attained is
Hence , Half of the maximum height is
From half of maximum height to maximum height :
Change in momentum from half of maximum height to maximum height :
Q. Two persons P and Q crosses the river starting from point A on one side to exactly opposite point B on the other bank of the river. The person P crosses the river in the shortest path. The person Q crosses the river in shortest time and walks back to point B. Velocity of river is 3 kmph and speed of each person is 5 kmph w.r.t river. If the two persons reach the point B in the same time, then the speed of walk of Q is.
(a) 13 kmph
(b) 12 kmph
(c) 14 kmph
(d) 11 kmph
Sol: Let d = width of river
Time taken to cross the river in shortest path by person P is
Time taken to cross the river in shortest time by person Q is
According to question
; Where Δt = time taken by person to come to the point B.
Q. A swimmer crosses a flowing stream of width ‘d’ to and fro normal to the flow of the river in time t1. The time taken to cover the same distance up and down the stream is t2. If t3 is the time the swimmer would take to swim a distance 2d in still water, then relation between t1, t2 & t3.
Sol: Let u = velocity of swimmer
v = velocity of river
Q. Two stones are projected from the top of a tower in opposite direction, with the same velocity v but at 30° & 60° with horizontal respectively. The relative velocity of first stone relative to second stone is