A rocket has taken off and is rising vertically according to the position equation, s = 50t^2 (use this to find the “given” rate of change). It is being tracked by a device located 2000 ft from the point of lift-off. The angle θ (in radians) is the angle between the tracking line and the ground. Find the rate of change in the angle θ , 10 seconds after lift-off. (a) GIVEN: Use the position function to find the given rate of change at t = 10 sec. (b) FIND: Write the derivative you want to find. (c) Write an equation relating the variable θ and two sides of the triangle. Then, differentiate with respect to time. (d) Solve for the unknown derivative in (b) after substituting in known values. Note: first you will need to solve for both s and the length of the hypotenuse at t = 10 sec.. Use a calculator for your final computations.
A rocket has taken off and is rising vertically according to the position equation, s = 50t^2 (use this to find the “given” rate of change). It is being tracked by a device located 2000 ft from the point of lift-off. The angle θ (in radians) is the angle between the tracking line and the ground. Find the rate of change in the angle θ , 10 seconds after lift-off.
(a) GIVEN: Use the position function to find the given rate of change at t = 10 sec.
(b) FIND: Write the derivative you want to find.
(c) Write an equation relating the variable θ and two sides of the triangle. Then, differentiate with respect to time.
(d) Solve for the unknown derivative in (b) after substituting in known values. Note: first you will need to solve for both s and the length of the hypotenuse at t = 10 sec.. Use a calculator for your final computations.
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