Question

A baseball is hit so that it travels straight upward after being struck by the bat. A fan observes that it takes 2.90 s for the ball to reach its maximum height.
a) Find the ball's initial velocity.


(b) Find the height it reaches

Answer 1

If the ball has initial velocity u and is subject only to the force of gravity, what is the equation for the velocity v at time t?

v = (something involving u, g and t) ... what is this expression?

Answer 2

If you're really, really stuck, go back to first principles and definitions.

Acceleration is by definition the change of velocity with respect to time. Here the velocity changes from u --> v over time t, and you know it is decelerating at a rate of -g. Therefore
\[ Acceleration = \frac{change \ in \ velocity}{change \ in \ time} = \frac{v - u}{t} = -g \]

Hence
\[ v - u = -gt \]
and
\[ v = u - gt \]

Now, that being the case, for what value of t is v = 0?