Final answer:
To determine when a rock hits the ground based on the given quadratic equation, we solve for t when the distance d is zero. The provided options do not match the solution of the quadratic equation. Without additional context, such as the cliff's height or initial conditions, we cannot accurately determine the time it takes for the rock to hit the ground.
Step-by-step explanation:
The question asks, 'A rock is dropped from the edge of a cliff. The equation below gives the distance, d, the rock travels in t seconds: d = 5t^2 + 5t. In how many seconds will the rock hit the ground?' This is a problem involving quadratic equations, which is a part of high school mathematics curriculum. To find when the rock hits the ground, we must solve for t when d is zero.
The given equation is d = 5t^2 + 5t. Setting d to zero for when the rock hits the ground, we get:
0 = 5t^2 + 5t.
Solving this equation (which can be simplified to t(5t + 5) = 0), we find that the rock hits the ground when t = 0 seconds or when t = -1 second. However, negative time is not possible in this context, so we disregard that value. The rock is already at the ground at t = 0 seconds, which means the equation doesn't represent the physical situation properly without further context like the height of the cliff or initial velocity.
This implies that the options provided (2, 3, 5, and 6 seconds) do not relate to the solution correctly unless additional information is given. To solve this type of problem accuratly, we would typically set up the equation considering the laws of physics governing free fall, like d = ½gt^2 where g eis the acceleration due to gravity (9.8 m/s2). Without that information, we can't determine the correct time it takes for the rock to hit the ground from the given options.