A penny is dropped from the top of a 345 foot building. Time is being measured in seconds.
A.) Write an equation that models the scenario
B.) How far is the penny from the ground after 2 seconds?
C.) How long does it take the penny to reach the ground?
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A.) To model the scenario, we can use the equation of motion for free fall:
y = h - 16t^2
where:
y is the height of the penny above the ground at any time t (in this case, t represents time in seconds),
h is the initial height of the penny above the ground (which is the height of the building in feet), and
16t^2 is the distance the penny falls due to gravity in t seconds. The factor of 16 is because acceleration due to gravity is approximately 32 ft/s^2, and this equation is derived from the formula y = h + v0t - 1/2gt^2, where v0 is the initial velocity (which is assumed to be 0 in this case for a dropped penny) and g is the acceleration due to gravity.
In this case, the equation for the scenario becomes:
y = 345 - 16t^2
B.) To find how far the penny is from the ground after 2 seconds, we substitute t = 2 into the equation and solve for y:
y = 345 - 16(2)^2
y = 345 - 16(4)
y = 345 - 64
y = 281
Therefore, the penny is 281 feet from the ground after 2 seconds.
C.) To find out how long it takes for the penny to reach the ground, we need to determine the value of t when y equals 0 (since the penny would be at the ground at that point):
0 = 345 - 16t^2
Solving this equation for t, we have:
16t^2 = 345
t^2 = 345/16
t^2 ≈ 21.5625
Taking the square root of both sides, we find:
t ≈ √(21.5625)
t ≈ 4.64
Therefore, it takes approximately 4.64 seconds for the penny to reach the ground.