A searchlight is 120 ft from a straight wall. As the beam moves along the wall, the angle between the beam and the perpendicular to the wall is increasing at the rate of 1.5 degrees divided by s. How fast is the length of the beam increasing when it is 130 ft long?

Question

A searchlight is 120 ft from a straight wall. As the beam moves along the​ wall, the angle between the beam and the perpendicular to the wall is increasing at the rate of 1.5 degrees divided by s. How fast is the length of the beam increasing when it is 130 ft​ long?

oobleck · Answer

1.5° = 0.026 radians so, if the length of the beam is x, then cosθ = 120/x when x = 130, sinθ = 5/13 -sinθ dθ/dt = -120/x^2 dx/dt Now just plug in the numbers and solve for dx/dt

A searchlight is 120 ft from a straight wall. As the beam moves along the​ wall, the angle between the beam and the perpendicular to the wall is increasing at the rate of 1.5 degrees divided by s. How fast is the length of the beam increasing when it is 130 ft​ long?

A searchlight is 120 ft from a straight wall. As the beam moves along the wall, the angle between the beam and the perpendicular to the wall is increasing at the rate of 1.5 degrees divided by s. How fast is the length of the beam increasing when it is 130 ft long?