A particle is thrown with velocity $u$ at an angle $α$ from the horizontal. Another particle is thrown with the same velocity at an angle $α$ from the vertical. What will be the ratio of times of flight of two particles?

Open in App

Solution

For first particles angle of projection from the horizontal is $α$
So $T_{1} = \frac{2 u sin α}{g}$
For second particle ,angle of projection from the vertical is $α$ . it mean from the horizontal is $(θ - α)$
$∴ T_{2} = \frac{2 u sin (90 - α)}{g} = \frac{2 u cos α}{g}$
So, ratio of time of flight $\frac{T_{1}}{T_{2}} = tan α$ .

Suggest Corrections

Similar questions

A particle is thrown with velocity u at an angle $α$ from the horizontal. Another particle is thrown with the same velocity at an angle $α$ from the vertical. The ratio of times of flight of two particles will be

Q. A particle is projected with a velocity

u,

at an angle

α,

with the horizontal. At what time its vertical component of velocity becomes half of its net speed at the highest point will be

Q. A particle is projected with a velocity

u

, at an angle

α

with the horizontal. Time at which its vertical component of velocity becomes half of its net speed at the highest point will be

Q. A particle is projected with a velocity

u

, at an angle

α

, with the horizontal. Time at which its vertical component of velocity becomes half of its net speed at the highest point will be

Q. Particle A is released from a point P on a smooth inclined plane inclined at an angle

α

with the horizontal. At the same instant another particle B is projected with initial velocity

u

making an angle

β

with the horizontal. Both the particles meet again on the inclined plane. Find the relation between

α

and

β

Join BYJU'S Learning Program

A particle is thrown with velocity u at an angle α from the horizontal. Another particle is thrown with the same velocity at an angle α from the vertical. What will be the ratio of times of flight of two particles?

For first particles angle of projection from the horizontal is αSo T1=2usinαgFor second particle ,angle of projection from the vertical is α. it mean from the horizontal is (θ−α)∴T2=2usin(90−α)g=2ucosαgSo, ratio of time of flight T1T2=tanα.

A particle is thrown with velocity $u$ at an angle $α$ from the horizontal. Another particle is thrown with the same velocity at an angle $α$ from the vertical. What will be the ratio of times of flight of two particles?