Q22 of 43 Page 85

A particle is projected upwards. The times corresponding to height h while ascending and descending are t1 and t2 respectively. Find the velocity of projection.

Given: Time of Ascent =

Time of Descent =


Acceleration = a = –g


(Negative due to opposite direction)


Let h be the height attained and u be the initial velocity


Now, using equations of motion:






This is a quadratic equation and, this will have two solution.


The two solutions will be and, because and are the two times taken to cover distance h.


So, and are two roots of the equation.



Now, using the properties of roots:


..1


..2


From 1:



From 2:



More from this chapter

All 43 →
20

A particle is projected with a velocity u at an angle θ° with the horizontal at any instant. Its velocity v is at right angles to its initial velocity u then v is

(a) u cos θ°


(b) u tan θ°


(c) u cot θ°


(d) u sec θ°

 21

Rain is falling vertically with a speed of 35 ms–1. A woman rides a bicycle with a speed of 12 ms–1 in the east to west direction. In which direction should she hold her umbrella?

 23

A person moves 30 m north and then 20 m east and finally 30√2 m south-west. What is the displacement from the original position?

 24

Two forces F1 and F2 are acting on a body. One force is double that of the other force, and the resultant is equal to the greater force. Then the angle between the two forces is?