Question

A body is projected horizontally with a speed v Find the velocity of the body when it covers equal distances
in horizontal and vertical directions.
(1) u=2v
(2)u=√5v
(3)u=√3v
(4)u=v/2​

it's answer is 2 please give correct explanation for answer.

Answer 1

Explanation:

h(y)=u(y).t+a(y).t²2h(y)=u(y).t+a(y).t²2

h(y)=0−gt²2h(y)=0−gt²2, a(y) = -g (‘-’ is showing direction)

h(y)=−gt²2...(1)h(y)=−gt²2...(1)

Also,

s(x)=v°t...(2)s(x)=v°t...(2)

To calculate velocity when body covers equal horizontal and vertical distance.

Equating (1) & (2),

s(x)=h(y)s(x)=h(y)

This gives, t=2v°gt=2v°g

v(y)=u(y)−gt(y)=u(y)−gt

v(y)=0−g.2v°gv(y)=0−g.2v°g

v(y)=−2v°v(y)=−2v°

v(x)=v°v(x)=v° (No acceleration in x direction)

v=v(x)+v(y)v=v(x)+v(y)(in vector form)

|v|=v(x)²+v(y)²−−−−−−−−−−−√|v|=v(x)²+v(y)²

|v|=(v°)²+(2v°)²−−−−−−−−−−−−√|v|=(v°)²+(2v°)²

|v|=v°5–√.|v|=v°5.

Hope it helps you!