Astone is dropped from the upper observation deck (the space deck) of the cn tower, 450 m above the ground. a. find the distance of the stone above ground level at time t. b. how long does it take the stone to reach the ground? c. with what velocity does it strike the ground? d. if the stone is thrown downward with a speed of 5 m/s, how long does it take to reach the ground?

A) The stone moves along the vertical direction by unifom accelerated motion, with acceleration equal to g (gravitational acceleration), starting from initial position h above the ground and with initial velocity equal to zero. So, its vertical position follows the law:


b) The time the stone takes to reach the ground is the time t at which its vertical position y(t) becomes zero:

and if we solve it, we find


c) Since it is a uniform accelerated motion, the velocity of the stone at time t is given by

where the initial velocity is zero: . The stone hits the ground at t=9.6 s, so its velocity at that time is

where the negative sign means it is directed downward.

d) In this case, since the initial velocity is not zero, the position at time t is given by

where  is the initial velocity.
The time the stone takes to reach the ground is the time t such that y(t)=0, so we have:

and by solving this equation, we find