A stone is projected in the air vertical upward with an initial velocity of 5m/s

Find a) tr and tf
b) H, highest distance has reached
c) where is the stone has reached after t=5.0sec

I have no idea what you mean by tr and tf

highest distance:
PotentialEnergyatTop=KE at bottom
mgh=1/2 mv^2
H= 1/2 (5^2)/9.8 m

at t=5 seconds
h(5)=H(0)+vi*5- 1/2 9.8 *5^2
= 25-4.9*25...looks like it is well below ground...

Time of rise, time of fall :)

To find the answers to your questions, we'll use the equations of motion for an object in free fall. These equations are:

1. Tr = (2 * Vo) / g (Time of rise)
2. Tf = 2 * Tr (Total time of flight)
3. H = (Vo^2) / (2 * g) (Maximum height)
4. d = Vo * t - (1/2) * g * t^2 (Distance traveled at time t)

Given:
Initial velocity (Vo) = 5 m/s
Acceleration due to gravity (g) = 9.8 m/s^2
Time (t) = 5.0 seconds

a) Finding tr and tf:
Using the equation 1:
Tr = (2 * Vo) / g
Substituting the given values:
Tr = (2 * 5) / 9.8
Tr ≈ 1.02 seconds

Using the equation 2:
Tf = 2 * Tr
Tf = 2 * 1.02
Tf ≈ 2.04 seconds

Therefore, tr ≈ 1.02 seconds and tf ≈ 2.04 seconds.

b) Finding H (maximum distance reached):
Using the equation 3:
H = (Vo^2) / (2 * g)
Substituting the given values:
H = (5^2) / (2 * 9.8)
H ≈ 1.28 meters

Therefore, the stone has reached a maximum height of approximately 1.28 meters.

c) Finding where the stone has reached after t = 5.0 seconds:
Using the equation 4:
d = Vo * t - (1/2) * g * t^2
Substituting the given values:
d = 5 * 5 - (1/2) * 9.8 * (5^2)
d = 25 - 122.5
d ≈ -97.5 meters

The negative sign indicates that the stone is below the starting point. Therefore, the stone has reached approximately 97.5 meters below its initial position after 5.0 seconds.