# calculus

A searchlight rotates at a rate of 4 revolutions per minute.?
The beam hits a wall located 13 miles away and produces a dot of light that moves horizontally along the wall. How fast (in miles per hour) is this dot moving when the angle between the beam and the line through the searchlight perpendicular to the wall is pi/6? Note that dtheta/dt=4(2pi)=8pi.

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. velocity= dtheta/dt * distance

in the units you have, with distance in miles, and dt in minutes, velocity will be in miles/minute

1. 👍
2. 👎
3. ℹ️
4. 🚩
👤
bobpursley
2. θπ

cos(π/6)=sqrt(3)/2
sec^2(π/6)=4/3

tan(θ)=x/13
x=13 tan(θ)
dx/dt=13 sec^2(θ) dθ/dt

At θ=π/6

dx/dt=13*(4/3)*8π=435.6 miles/min = 26138 miles/hr

1. 👍
2. 👎
3. ℹ️
4. 🚩
3. Note to above attempt: velocity in x-direction, not radial velocity.

1. 👍
2. 👎
3. ℹ️
4. 🚩

## Similar Questions

1. ### physics

A space station, in the form of a wheel 110 m in diameter, rotates to provide an "artificial gravity" of 3.00 m/s2 for persons who walk around on the inner wall of the outer rim. Find the rate of rotation of the wheel (in

2. ### Physics

A uniform beam of length 1.0 m and mass 16 kg is attached to a wall by a cable that makes an angle of 30 degrees with the end of the beam, as shown in the figure. The beam is free to pivot at the point where it attaches to the

3. ### physics

A uniform 8 m 1500 kg beam is hinged to a wall and supported by a thin cable attached 2 m from the free end of the beam as shown in the figure. The beam is supported at an angle of 30 degrees above the horizontal. a) free diagram

4. ### TRIG

A circular power saw has an 8-1/2 inch diameter blade that rotates at 4400 revolutions per minute. a)Find the angular speed of the saw blade in radians per minute. b)Find the linear speed in feet per minute of one of the 24

1. ### physics

the figure shows a uniform beam of weight 420 N and length 2.0 m suspended horizontally. On the left it is hinged to a wall, on the right it is supported by a cable bolted to the wall at distance D above the beam. The least

2. ### Calculus

A vehicle moves along a straight path with a speed of 4m/s. A searchlight is located on the ground 20m from the path and is kept focused on the vehicle. At what rate (in rad/s) is the searchlight rotating when the vehicle is 15

3. ### trig

A wheel with a 24-inch diameter is turning at the rate of 32 revolutions per minute. To the nearest inch per minute, what is the linear velocity of a point on the rim?

4. ### Physics

A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of mb = 6.1 kg and the sign has a mass of ms = 16.4 kg. The length of the beam is L = 2.83 m. The sign is attached at the very end of the beam, but the

1. ### physics

During the spin cycle of a washing machine, the clothes stick to the outer wall of the barrel as it spins at a rate as high as 1800 revolutions per minute. The radius of the barrel is 26 cm. a. Determine the speed of the clothes

2. ### physics

A uniform horizontal beam with a length of 8m and a weight of 200N is attached to a wall by a pin connection. Its far end is supported by a cable that makes an angle of 53° with the beam (Figure below). If a 600N person stands 2m

3. ### physics

In Fig. 12-51, uniform beams A and B are attached to a wall with hinges and loosely bolted together. Beam A has length LA = 2.55 m and mass 49.0 kg; beam B has mass 69.0 kg. The two hinge points are separated by distance d = 1.86

4. ### physics

an astronaut rotates at the end of a test machine whose arm has a length of 10.0m. if the acceleration she experiences must not exceed 5g (g=10m/s^2? what is the maximum number of revolutions per minute of the arm?