A stone is thrown vertically upwards with an initial velocity of 30meter per second from the top of a tower 20metes high find the time taken to reach the maximum height and the total time which elapses before it reaches the ground and gravity is 10meter per second.

3 seconds to reach maximum height

3.61 seconds to go from maximum height to the ground

6.61 seconds for the whole thing

Explanation:

Since the question states the stone is thrown vertically we can neglect using trigonometry for component vectors and can just use the given values.

At the top of the arc the velocity will instantaneously be at zero, therefore the final velocity for this is 0.

Since we know final velocity(Vf) , initial velocity(V0), and acceleration(a) we can find the time(t) using this equation:

Vf = V0 + at

0 = 30 + (-10)t

t = 3 seconds

*acceleration is negative in this case because we assume that acceleration due to gravity is positive when acting downwards. in this case since the gravitational force is acting against the object the acceleration due to gravity is negative

Next: to find total time I am going to find the total distance it needs to travel to get down to the ground by adding the distance it traveled upward to the height of the tower

the distance traveled upward can be found using this equation:

Vf^2 = V0^2 + 2ad

0^2 = 30^2 + 2(10)d

d = 45m

Then add 45m to the height of the tower(20m) to get 65m total distance = 65m

Now I can find total time needed by plugging into this equation:

d = V0*t + (1/2)a*t^2

*note that since we are starting from the maximum height now: V0 = 0

65 = 0*t + (1/2)(10)t^2

65 = 5t^2

t = 3.61 seconds