1. The height at time t (in seconds) of a mass, oscillating at the end of a spri

Question

1. The height at time t (in seconds) of a mass, oscillating at the end of a spring, is s(t) = 300 + 80 sin t cm. Find the velocity and acceleration at t = 3 s.

v(pi/3) = ? (cm/sec)

a(pi/3) = ? (cm/sec^2)

2. A man on the sixth floor of a building sees a bucket (dropped by a window washer) pass his window and notes that it hits the ground 1 second later. Assuming a floor is 5 m high and the window is in the middle of the sixth floor, from what floor was the bucket dropped? (Round your answer up to the next whole number.)

3.Suppose (t) measures the minimum angle between a clock's minute and hour hands. What is '(t) at 9 o'clock?

Explanation / Answer

1)height s(t)= 300 + 80sin t

velocity v(t)=ds/dt =0+80cost

velocity v(pi/3)=80cos(pi/3)

velocity v(pi/3)=80(1/2)

velocity v(pi/3)=40 cm/sec

acceleration a(t)=dv/dt =-80sint

a(pi/3) =-80sin(pi/3)

a(pi/3) =-80(3 /2)

a(pi/3) =-403

a(pi/3) =-69.3cm/sec^2

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