From the top of a tower 40 m high a ball is projected upwards with a speed of 20 ms -1 at an angle 30° with the horizontal. The ratio of the total time of flight to hit the ground to the time taken by it to come back to the same initial elevation (g = 10 `ms^(-2)` ) is :

Options

A. `3:2`
B. `4:1`
C. `3:1`
D. `2:1`

Answer

D

Explanation

Time taken to reach point (C ) is
`T=(2usintheta)/g=(2xx20xx1/2)/10=2`sec
Time taken to go from C to D is
`h=ut + 1/2g t^(2)`, Initial vertical velocity= `20sin30^@`
`40=20xx1/2xxt +5t^(2)`
`implies t^(2)+4t -2t-8=0`
r(t + 4)-2(t + 4) = 0
(r + 4) (r-2) = 0
`implies` t = 2 s as time cannot be negative.

`:.` Time taken to go from A to D= 2+2=4s
`:.` ratio of timings = `4/2=2:1`