how far can you get?
Let’s suppose you throw a ball straight up with an initial speed of 50 feet per second from a height of 6 feet.
- Find the parametric equations that describe the motion of the ball as a function of time.
- How long is the ball in the air?
- Determine when the ball is at maximum height. Find its maximum height.
There are two ways to get your maximum height:
Method 1 (requires calculus)
i assume you ahve a parametric equation for the vertical motion like: y=f(t)
differentiate and find the value of t where . This will give you the time at which the ball is at its maximum height.
The height at that moment is then f(t).
Method 2
Consider the vertical motion of the ball only and use one of Newton's equations of motion:
v = 0 (at maximum height, it is no longer gaining altitude)
u = ? (should have been given in question)
a = accelleration (you should know the value of this!)
t = the time at which max height is reached (solve for this)
Then use another equation to get the height at this moment, eg