A ball is thrown vertically upward with a speed of 26.3m/s. How high does it rise? How long does it take to reach its highest point? How long does...

The answer given above is correct. However the problem can be solved using easier method.

The ball is thrown up with velocity u = 26.3 m/s

While travelling up the velocity of ball slows down till it reaches velocity v = 0 at its highest point.

The acceleration of ball due to gravitational pull a = 9.8 m/s^2

Thus total reduction in velocity when the ball reaches its highest point = v.

Therefore time taken to reach highest point t = v/a =26.3/9.8 = 2.6837 s (approximately)

The height to which ball rises s = t*(v + u)/2 = 2.6837*26.3/2 = 35.2093

We do not need to make separate calculations for the return path of the ball from highest point to the point to the starting level, as the velocities are exactly equal and opposite those of the upward journey.

Therefore velocity of ball when it returns to the starting level = -26.3 m/s.

Assuming starting point of the ball was the ground level, the time taken by ball to reach ground after it reaches the highest point = 2.6837 s