A man is riding on a horse. He is trying to jump the gap between two symmetrical ramps of snow separated by a distance W as shown in figure. He launches off the first ramp with a speed `v_L`. The man and the horse have a total mass m. and their size is small as compared to W. The value of initial launch speed `V_(L)` which will put the horse exactly at the peak of the second ramp is

Options

A. `sqrt((Wg)/(sintheta xx costheta))`
B. `sqrt((Wg)/(sin(theta//2) xx cos(theta//2))`
C. `sqrt((Wg)/(2sintheta costheta))`
D. `sqrt((2Wg)/(sintheta costheta))`

Answer

C

Explanation

c. Due to symmetry, the maximum of the trajectory lies halfway
across the gap.
Therefore, range of projectile motion

`=W`
`rArr W = (2V_(L)^(2) sin theta cos theta)/g`
`:. VL = sqrt((Wg)/(2sinthetacostheta))`