Answer:
The student should have divided the amount after the discount by the percentage expressed as a decimal.
Step-by-step explanation:
H(t) = -16t² + 704t = -16(t² - 44t)
Transforming to vertex form: -16(t² - 44t + 484) + 704
h(t) = -16(t - 22)² + 704
The projectile reaches its peak height after 22 seconds, corresponding to the vertex of the parabola at (22, 704).
Answer:
The height is 11.76 meters.
Step-by-step explanation:
To solve this problem, the following equations are necessary:
The first one relates initial and final velocities, taking into account that gravity is 9.81 m/s² and the time is 0.3 seconds:
Vf = Vo + g * t = Vo + 9.81 * 0.3
Vf = Vo + 2.94 (1)
The second one also connects initial and final velocities, but this time with distance S, which we know to be 5 meters:
Vf² = Vo² + 2 * g * S
Vf² = Vo² + 2 * 9.81 * 5
Vf² = Vo² + 98.1 (2)
We now have two equations with two unknowns. By substituting (1) into (2):
(Vo + 2.943)² = Vo² + 98.1
Vo² + 5.886 * Vo + 8.66 = Vo² + 98.1
Canceling Vo² and rearranging gives us:
Vo = 89.44 / 5.886
Vo = 15.195 m/s
Now using the formula:
Vo² = 2 * g * h
h = Vo² / (2 * g) = (15.195²) / (2 * 9.81) = 11.76 meters
So, the height corresponds to 11.76 meters.
