Question

Lin and Clare were standing in the woods near a stream, and each threw a stone up in the air at the same time so that it would land in the water. The graph represents the height of a stone t seconds after it was tossed up by Lin. The function f given by f(t) = (-16t^2)(t-1) represents the height of a stone t seconds after it was thrown by Clare. In both functions, height is measured in feet. Whose stone hit the water first? When did that happen?

A) Lin's stone hit the water first, and it happened at t = 0.5 seconds.
B) Clare's stone hit the water first, and it happened at t = 1 second.
C) Lin's stone hit the water first, and it happened at t = 1 second.
D) Clare's stone hit the water first, and it happened at t = 0.5 seconds.

Answer 1

By calculating when Clare's stone hits the water using her stone's height function, we find that it occurs at t = 1 second. Without Lin's stone's graph, we cannot determine the exact time hers hits the water, but Clare's stone hits the water at t = 1 second as per the given function. option (A)

Step-by-step explanation:

To determine whose stone hit the water first, we need to examine the functions given for Lin's stone (represented by the graph, not explicitly provided) and Clare's stone, for which the function is f(t) = (-16t^2)(t-1). The stones hit the water when their height is at 0 feet, meaning we need to solve for t when f(t) equals zero for Clare's stone.

Clare's stone's height over time is specified by a quadratic equation. We can factor the given equation:

f(t) = (-16t^2)(t-1) = -16t^2 + 16t

To find when Clare's stone hits the water, we solve for t when f(t) = 0:

0 = -16t^2 + 16t

t(-16t + 16) = 0

t = 0 (at launch) or t = 1 second (when it hits the water)

Since Lin's stone's graph isn't provided, we cannot find the exact moment it hits the water. However, we can conclude that if Clare's stone hits the water at t = 1 second, then the correct answer must be the one that corresponds with Clare's stone's function, which is option B: Clare's stone hit the water first, and it happened at t = 1 second.