<span>First question: The type of energy involved when a river moves sediment and erodes its banks is: option d. Kinetic energy. Kinetic energy is the energy associated with motion. A body (in this case the water) that moves has an energy associated with its motion that is proportional to the speed (exactly to the square of the speed). When the water collides with the banks it is the kinetic energy of the river that erodes it Second question: the answer is the option d. As gravity pulls water down a slope potential energy changes to knietic energy. This is the, water loses altitude and gains velocity. The potential energy. which is proportional to the height, decreases and the kinetic energy, which is proportional to the square of the speed, increases.</span>
The height at time t is given by
h(t) = -4.91t² + 34.3t + 1
When the ball reaches maximum height, its derivative, h'(t) = 0.
That is,
-2(4.91)t+34.3 = 0
-9.82t + 34.3 = 0
t = 3.4929 s
Note that h''(t) = -9.82 (negative) which confirms that h will be maximum.
The maximum height is
hmax = -4.91(3.4929)² + 34.3(3.4929) + 1
= 60.903 m
Answer:
The ball attains maximum height in 3.5 s (nearest tenth).
The ball attains a maximum height of 60.9 m (nearest tenth)