A baseball is hit straight up from an initial height of 3 feet with an initial velocity of 65 ft/sec.

Question

a. Write a set of parametric equations that models the height (vertical) of the ball as a function of time t. x(t) and y (t)

Graph the parametric equations for 0 ≤ t ≤ 5. Sketch the graph.

c. What is the maximum height of the ball? ____________

e. How many seconds does it take to reach its maximum height? ____________

f. When does the ball hit the ground? _______________

Answer 1

(a)

y(t) = -16t² + 65t + 3 (t in seconds, h in feet)

x(t) = 0 (if hit straight up)

This forum is not suitable for graphing.

(c) Maximum height occurs at the vertex of the height-vs.-time parabola, which is at

t = -65/[2(-16)] s = ? s

Evaluate y(t) at this value of t to get maximum height.

(e)

t = -65/[2(-16)] s = ? s

(f)

Set h(t) = 0 and solve the resulting quadratic equation for t using the quadratic formula. You will get a negative and a positive solution. Since time starts at t = 0, the positive solution is the correct one.