A rocket is projected vertically upwords. It explodes at the/ topmost point of its trajectory into three identical fragments . One of the fragments comes straight down in time t 1 while the1 other two land at a time `t_(2)` after explosion. Find the height at which the explosion ocurred in terms of `t_(1) and t_(2)` ?

A stone is projected vertically upwards. Its height h at time t sec is h=(80)t-(16)t^(2) . The velocity with which it hits the ground is

A train accelerates from at the constant rate b for time t_(2) at a constant rate a and then it retards at the comes to rest. Find the ratio t_(1) // t_(2) .

A body is projected verticallt upwards. If t_(1) and t_(2) be the times at which it is at a height h above the point of projection while ascending and descending respectively, then:

A shell is fixed from a cannon with a speed of 100 m//s at an angle 60^(@) with the horizontal (positive x-direction). At the highest point of its trajectory, the shell explodes into two equal fragments. One of the fragments moves along the negative x-direction with a speed of 50 m//s . What is the speed of the other fragment at the time of explosion.

A shell is fired from a cannot with a speed of 100ms^(-1) at an anlge 60^(@) with the horizontal (x-direction). At the highest point of its trajectory the shell explodes into two equal fragments. One of the fragments moves along the negative x-direction with a speed of 50 ms^(-1). What is the speed of the other fragment at the time of explosion ?

A shell is fired from a cannon with a speed of 100 m//s at an angle 60^(@) with the horizontal (positive x -direction). At the highest point of its trajectory, the shell explodes in to two equal fragments. One of the fragments moves is the speed of the other fragment at the time of explosion.

A particle is projected vertically upwards from a point O on the ground. It takes time t_(1) to reach a point A at a height h above the ground, it continues to move and takes a time t_(2) to reach the ground. Find (a) h, (b) the maximum height reached and (c ) the velocity of the partical at the half of maximum height.