Question

When a body is projected from a level ground the ratio of its speed in the vertical and horizontal
direction is 4:3. If the velocity of projection is u, the time after which, the ratio of the velocities in the
vertical and horizontal directions are reversed is
1)7u/20g
2)35u/10g
3)9u/g
4)10u/g​

Answer 1

Method 1:

uyux=43⇒tanθ=43⇒sinθ=45 .

Further vyvx=34⇒vyux=34⇒vxuy=43(sincevx=ux)

Let us multiply the two fractions

uyux.vxuy=34=43.43

Or, vy=916uy

Now from vy=uy−gt, we have

916uy=uy−gt

Or, t=716uy. But uy=usinθ=4u5

⇒t=7u20g

So the answer is 7u/20g