A stone is thrown upward from ground level. The initial speed is 32 ft/sec. (a) In how many seconds will the stone hit the ground?(b) How high will...

The stone thrown upwards will slow down under the influence of
gravity till it reaches 0 velocity/speed and will again start falling down with increasing
velocity in downward direction till it hits the ground. The magnitude of velocity at the time of
hitting the ground will be same as the velocity at which the stone was thrown. The acceleration
of the stone due to gravity is equal to 32 feet/s^2.

Thus we can
find the answer to the given questions as
follows:

(a)

Acceleration due to
gravity = a = 32 feet/second^2

Upward velocity = u = 32
feet/s

Final velocity when the stone reaches its highest point = v =
0

Time take t o reach highest point = t = (u -v)/a = 32/32 = 1
s

The stone will take the same time to fall down and hit the ground.
Therefore:

The taken by stone to hit the ground = 1 + 1 = 2
seconds

(b)

Distance travelled by stone
on upward travel = d = ut/2

= 32*1/2 = 16
feet

The stone will go up 16 feet
high.

(c)

Distance of highest point
reached by stone is given by:

Distance travelled =
(a*t^2)/2

When the stone to travel 36 feet
high:

36 = (32*t^2)/2

t^2 = 36/16 =
2.25

Therefore:

t = 1.5
s

As the stone takes 1.5 seconds to reach 0
velocity:

Initial velocity = t*a = 1.5*32 = 48
feet/s

Answer:

Minimum required speed
for stone to reach a height of at least 36 feet = 48 feet/s