The motion of the projectile

Question

I've got the following $$h(t) = -\frac{1}{2} gt^2 + Vt + h'$$ where $h'$ and $V$ are the initial height and velocity of the object, respectively. Suppose a person standing at the top of the tower of pisa ($176$ft high) throws a ball directly upward with an initial speed of $96$ft/s. Find the ball's height, its velocity and acceleration at time.

Answer 1

Here's how you can solve this problem:

• For the height, just plug in whatever $t$ is into the formula for $h(t)$.
• For the velocity, because of gravity, the velocity decreases by $g$ for every second, so it decreases by $gt$ for every $t$ seconds. Thus, we get $v(t)=V-gt$, so to get the velocity, just plug in whatever $t$ is into that formula.
• The acceleration is $a(t)=-g$ regardless of time as that is the acceleration due to gravity.