91Ó°ÊÓ

When gravity first exerts force on an item, its initial velocity indicates how fast it travels. The final velocity, on the other hand, is a vector number that measures a moving body's speed and direction after it has reached its maximum acceleration.

The initial velocity in y direction we need to calculate.

The time is also not given.

The displacement in y direction is$0.75$meter.

The gravitational acceleration is -$9.8$m/s²

The final velocity is also known to be 0.

(a) The velocity in the x frame will be constant in all time. Considering the initial velocity

$\begin{array}{rcl}{V_{fy}}^2& =& {V_{iy}}^2+2aY\\ 0^2& =& {V_{iy}}^2+2\left(-9.8\right)\left(0.75\right)\\ {V_{iy}}^2& =& 14.7\\ V_{iy}& =& Â\pm 3.91 m/s\\ & & \end{array}$

The initial velocity will be positive, that is $3.83$m/s.

(b) The time can be calculated by following equation

$\begin{array}{rcl}{V}_f& =& V_i+at\\ 0& =& 3.87+\left(-9.8\right)t\\ t& =& 0.391 s\\ & & \end{array}$

Hence the time taken is$0.391$S.

He should begin his jump in below distance

$\begin{array}{rcl}\stackrel{¯}{V}& =& \frac{x}{t}\\ 5& =& \frac{x}{0.391}\\ x& =& 1.96 meter\\ & & \end{array}$

He should begin his jump in below distance of $1.96$meter.