a The rocket's height h in meters is given by the equation h=- 4.9t^2+56t, where t is the time in seconds after the launch. Let's plot the parabola h=- 4.9 t^2+56t.
We are asked to find the maximum height the rocket will reach. Since the parabola open downwards, the maximal value is at the vertex. First, we will find the t-coordinate of the vertex, p.
p=-b/2a
The values of a and b are the coefficients in front of t^2 and t, respectively. This tells us that a=-4.9 and b=56. Now, let's find the t-coordinate of the vertex.
Therefore, the maximum height the rocket will reach is about 479.52 meters.
b We are asked to find the time that the rocket will reach its maximum height. From Part A we know that this is p≈ 5.71 seconds.
c From Part B we know that after about 5.71 seconds the rocket will reach its maximum height from the ground level. Therefore, after another 5.71 seconds the rocket will reach the ground level. Therefore the rocket will land after about 5.71+5.71=11.42 seconds.
