30-60-90 triangle..find the value of y ?
1 answer:
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Question:
A silver coin is dropped from the top of a building that is 64 feet tall. the position function of the coin at time t seconds is represented by
s(t) = -16t² + v₀t + s₀
Determine the position and velocity functions for the coin.
Answer:
<em>position function:</em><em> s(t) = (-16t² + 64) ft</em>
<em>velocity function:</em><em> v(t) = (-32t) ft/s</em>
Step-by-step explanation:
Given position equation;
s(t) = -16t² + v₀t + s₀ ---------(i)
v₀ and s₀ are the initial values of the velocity and position of the coin respectively.
(a) Since the coin is dropped, the initial velocity, v₀, of the coin is 0 at t = 0. i.e
v₀ = 0.
Also since the drop is from the top of a building that is 64 feet tall, this implies that the initial position, s₀, of the coin is 64 ft at t=0. i.e
s₀ = 64ft
Substitute the values of v₀ = 0 and s₀ = 64 into equation (i) as follows;
s(t) = -16t² + (0)t + 64
s(t) = -16t² + 64
Therefore, the position function of the coin is;
<em>s(t) = (-16t² + 64) ft</em>
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(b) To get the velocity function, v(t), the position function, s(t), calculated above is differentiated with respect to t as follows;
v(t) =
v(t) =
v(t) = -32t + 0
v(t) = -32t
Therefore, the velocity function of the coin is;
<em>v(t) = (-32t) ft/s</em>
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