Question

With what speed a body be thrown upwards so that the distance traversed in $5^{th}$ second and $6^{th}$ seconds are equal?

• A. $5.84m/s$
• B. $49m/s$
• C. $\sqrt{98}m/s$
• D. $98m/s$

Answer 1

The correct option is B $49m/s$

Given,

A body is thrown upward at speed, u

At 5^th and 6^th distance travel is equal = $s$

Mean in 4sec to 5 sec distance travel = $s$

And in 5sec to 6 sec distance travel = $s$

It is only possible if body deaccelerated in 4sec to 5 sec and accelerated in 5sec to 6 sec

In projectile motion, this condition is suited, if in 4sec to 5 sec body go upward, and in 5sec to 6 sec body go downward.

So, at 5sec body is at top, and its vertical velocity is zero.

Acceleration of gravity, $g$

Time, $t$

Initial velocity, $u$

Final velocity, $v$

Apply kinematic equation at top position.

$v=u-gt$

$0=u-gt$

$u=gt=9.81\times 5=49.01m/s$

Hence, body thrown upward at speed $49m/s$