During volcanic eruption chunks of slid rock are blasted out of the volcano . (a) At what initial speed

Wou ld a valcanic object have to be ejected at `37^(@)` to the horizontal from the vent A in order to fall at B as shown in Fig. 5.22? (b) what is the time of flight? (g=9.8`m//s^(2)`)

Explanation

(a) Taking the point A as origin , with upward direction of motion postive and using the equation,
`s=ut+(1)/(2)at^(2)`
for horizontal motion: `x=u cos thetaxxt` ...(i)
and for vertical motion: `y=u sin thetaxxt-(1)/(2)g t^(2)`.....(ii)
Substituting r from Eqn. (i) in (ii),
`y=xtan theta-(g)/(2)[(x)/(u cos theta)]^(2)`
Here `y=3.3xx10^(3)m,x=9.4x10^(3)m` and `theta=37^(@)`
So, `-3.3xx10^(3)=9.4xx10^(3) tan 37^(@)-4.9[(9.4xx19^(3))/(u cos 37^(@))]^(2)`
or `(9.4xx10^(3))/(u cos 37^(@))=[(10.35xx10^(3))/(4.9)]^(1//2)=46 [tan37^(@)=(3)/(4)]`
or `u=(9.4xx10^(3))/(46xx(4//5))=(47000)/(184)=255m//s`
(b) Substituting the above value of u in Eqn. (i).
`t=(x)/(ucos theta)=(9.4xx10^(3))/(255xx(4//5))`
`=(9400)/(204)=46s`