Question

a body is projected vertically upwards . If t1 and t2 be the times , at which it is at a height h above the point of projection while ascending and descending respectively then maximum height reached by the body is​

Answer 1

ANSWER

Let v be initial velocity of vertical projection and t be the time taken by the body to reach a height h from ground.

Here, u=u,a=−g,s=h,t=t

Using, s=ut+

2

1

at

2

, we have

h=ut+

2

1

(−g)t

2

or gt

2

−2ut+2h=0

∴t=

2g

2u±

4u

2

−4g×2h

=

g

u±

u

2

−2gh

It means t has two values, i.e.,

t

1

=

g

u+

u

2

−2gh

t

2

=

g

u−

u

2

−2gh

t

1

+t

2

=

g

2u

or u=

2

g(t

1

+t

2

)

.

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