Question

A body projected at angle 'O' with the horizontal. If remains for a time T in air. Ita
horizontal range is R, then tan 0 =
1) gT/2R
2) gʻT/2R 3) gr/2R 4) g1/2R
laual ground with a velocity of 30 ms at 30° to the​

Answer 1

Explanation:

Given,

Time of flight is T

Range=R

So, Let a particle is projected with speed u at an angle θ with horizontal. after time t particle strikes the ground.

so, time of flight,

T=

g

2usinθ

Squaring both sides,

T

2

=

g

2

4u

2

sin

2

θ

......(1)

Range , R=

g

u

2

sin2θ

We know, sin2θ=2sinθ.cosθ

R=

g

2u

2

sinθcosθ

........(2)

Dividing equation (2) by (1),

T

2

R

=

2

g

cosθ

So, R∝T

2

Thus, we can see that range of the projectile is directly proportional to the square of time of flight.

so, if the time of flight is doubled keeping the angle of projection same then, the new range should be four times