The height metres of a small ball thrown upwards from ground level at time seconds is…
MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
The height h metres of a small ball thrown upwards from ground level at time t seconds is modelled by a quadratic polynomial. The ball leaves the hand at t=0 and returns to the ground at t=10. At t=2, its height is 24m.
(i) Taking h as a quadratic function of t, write it in factored form with an unknown leading coefficient k.
(ii) Find the value of k using the information given for t=2.
(iii) Express h in standard form and calculate the exact time at which the ball reaches its maximum height.
(iv) Determine this maximum height and interpret the x-intercepts and maximum point in the context of the motion.