Question

A superman is sitting on a tree 98m right with a baby he has rescued from the claws of a tiger. Unfortunately the child slips and fall with an initial velocity of 0ms^–². Superman realized what was happening 2 seconds later and flow to catch the child at a speed of 39.2ms^–¹. Calculate

(1) the time superman will fly before catching the child.

(2) the distance superman will fly before catching the child.

Answer 1

The equation of motion of a superman

$$y_s=39.2(t-2)$$

The equation of motion of a child

$$y_c=9.8t^2/2$$

At the instant when superman catches the child

$$y_s=y_c$$

$$39.2(t-2)=9.8t^2/2$$

$$t^2-8t+16=0$$

(1) the time superman will fly before catching the child:

$$\Delta t=4-2=2\:\rm s$$

(2) the distance superman will fly before catching the child:

$$y_s=39.2*2=78.4\:\rm m$$