A particle is moving with the given data. Find the position of the particle. a(t

Question

A particle is moving with the given data. Find the position of the particle. a(t) = cos t + sin t, s(0) = 8, v(0) = 1 A stone is dropped from the upper observation deck of a tower, 750 m above the ground. (Assume g = 9.8 m/s2.) Find the distance (in meters) of the stone above ground level at time t. How long does it take the stone to reach the ground? (Round your answer to two decimal places.) With what velocity does it strike the ground? (Round your answer to one decimal place.) If the stone is thrown downward with a speed of 8 m/s, how Iona does it take to^ reach the ground? (Round your answer to two decimal A car is traveling at 50 mi/h when the brakes are fully applied, producing a constant deceleration of 48 ft/s2. What is the distance covered before the car comes to a stop? (Round your answer to one decimal place.)

Explanation / Answer

8.

a(t) = cost +sint

=>

dv/dt = cost +sint

=>

v(t) = sint -cost +c

=>

v(0) = 1

=>

c = 2

=>

v(t) = sint-cost +2 = ds/dt

=>

s(t) = -cost -sint +2t +c

s(0) = 8

=>

s(t) = -cost -sint +2t +9

9.

(a)

h(t) = 750 -0.5*9.8^t^2 = 750 -4.9t^2

(b)

h(t) = 0

=>

750 = 4.9t^2

=>

t^2 = 750/4.9

=>

t = 12.37 s

(c)

velocity it strikes the ground = 9.8 t = 9.8 *12.37 = 121.24m/s

(d)

750 = 8t +4.9t^2

=>

t = 11.58s

11.

50mi/hr = 73.33 ft/s

=>

distance covered = (73.33)^2 / (2*48) = 56.01 ft

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