A rock is thrown straight down with an initial velocity of 17.5 m/s from a cliff. What is the rock's displacement after 2.0 s? (Acceleration due to gravity is 9.80 m/s2.)Select one:a.55 mb.28 mc.49 md.64 m
Question
A rock is thrown straight down with an initial velocity of 17.5 m/s from a cliff. What is the rock's displacement after 2.0 s? (Acceleration due to gravity is 9.80 m/s2.)Select one:a.55 mb.28 mc.49 md.64 m
Solution 1
To solve this problem, we can use the equation of motion:
d = vit + 0.5at^2
where: d = displacement vi = initial velocity a = acceleration t = time
Given: vi = 17.5 m/s (downwards, so we consider it negative) a = 9.8 m/s^2 (downwards, so we consider it negative) t = 2.0 s
Substituting these values into the equation:
d = (17.5 m/s)(2.0 s) + 0.5(-9.8 m/s^2)(2.0 s)^2
d = 35 m - 19.6 m
d = 15.4 m downwards
So, none of the options (a.55 m, b.28 m, c.49 m, d.64 m) match the calculated displacement. There might be a mistake in the question or the options provided.
Solution 2
To solve this problem, we can use the equation of motion:
d = v_it + 0.5a*t^2
where: d is the displacement, v_i is the initial velocity, t is the time, and a is the acceleration.
Given in the problem: v_i = 17.5 m/s, t = 2.0 s, and a = 9.80 m/s^2 (acceleration due to gravity).
Substituting these values into the equation:
d = 17.5 m/s * 2.0 s + 0.5 * 9.80 m/s^2 * (2.0 s)^2 d = 35 m + 0.5 * 9.80 m/s^2 * 4.0 s^2 d = 35 m + 19.6 m d = 54.6 m
So, the rock's displacement after 2.0 s is approximately 55 m. Therefore, the correct answer is a. 55 m.
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