Question

Please help me with this

Answer 1

Answer:

Explanation:

Use the one-dimensional equation for displacement:

Δx = v₀t + $\frac{1}{2}at^2$ where Δx is the displacement, v₀ is the initial velocity (which is 0 since someone had to be holding the penny still before it was dropped), t is the time it takes to travel a certain distance (which is given as 4 seconds), and a is the acceleration due to gravity which is -9.8 m/s/s. Filling in:

Δx = $(0\frac{m}{s})(4s)+\frac{1}{2}(-9.8\frac{m}{s^2})(4s)^2$ I'm going to expand this first so you can see how the units work out. First of all, anything times 0 is 0, so what is right in front of the plus sign goes to 0 and I'm going to leave it out. How this looks expanded without doing any of the actual math yet is:

Δx = $\frac{1}{2}(-9.8\frac{m}{s^2})(4^2s^2)$ which makes it apparent that the seconds-squared cancel each other out, leaving us with the meters only. NOW doing the math and rounding to 2 sigfig's even though there's only 1 in the number 4:

Δx = 78 m(the negative would only be used if the question we were answering was how far the penny had to fall, which would then use the negative sign to indicate that the penny is falling to a point that is below th point from which it was released. Since height is a distance measurement, it will never be negative. Keep in mind, asking how far the penny fell is not the same thing in physics as asking how tall the building was that the penny fell from.)