Answer:
-29.61m/s
Step-by-step explanation:
To find the average speed of the pencil after dropping it for 2.8 seconds, we start with the fall distance equation for the student, s(t) = −16t² + 8√t. First, we differentiate this function since velocity is the rate of change of distance with respect to time, expressed as
V = d(s(t))/dt
s(t) = −16t² + 8t^1/2
V = -32t + 1/2(8)t^(1/2 - 1)
V = -32t + 4t^-1/2
To find the average speed, we substitute t = 2.8 into the derived equation since the pencil reaches the ground precisely after 2.8 seconds.
V = -32t + 4(2.8)^-1/2
V = -32 + 4/√2.8
V = -32 + 4/1.6733
V = -32 + 2.391
v = -29.61m/s
Thus, the average speed at which it fell is -29.61m/s
Answer:
Step-by-step explanation:
First, we apply the Pythagorean theorem to determine the distance from Manuel’s home to the resort.
S1 = √50²+20²
S1 = √2500+400
S1 = √2900
S1 = 53.85m
Next, we find the distance from Manuel's home to his friend’s residence.
S2 = √15²+10²
S2 = √225+100
S2 = √325
S2 = 18.03m
The distance between the two boys and the resort will be represented as ∆S = S2 - S1.
∆S = 53.84 - 18.03
∆S = 35.81m
