Posted by **Isis** on Thursday, November 29, 2012 at 6:22pm.

a ball is thrown up and reaches a maximum height of 5 m.

a) what is the initial velocity of the ball?

b) how long does it take for the ball to reach its maximum height?

c) what is the final velocity of the ball? if i returns to where it was thrown from?

- physics -
**Jennifer**, Friday, November 30, 2012 at 6:15pm
y = y0 + v0*t - 1/2*g*t^2

where y0 is the initial height = 0, v0 is the initial speed, and g is the acceleration due to gravity, t is time, and y is the vertical position.

The ball reaches it's maximum height when dy/dt = 0 = v0 - g*t

and y = 5, so

5 = v0*t - 1/2*g*t^2

Use algebra to find the initial velocity and time.

The final velocity of the ball is given by

1. v = v0 - g*t, occurs when y = 0, or when

2. 0 = v0*t - 1/2*g*t^2

solve 2nd equation for t, and plug into 1st equation to solve for the final speed v at this time.

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